# bank maths questions for Preli Exam : AUST All

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## bank maths questions for Preli Exam সম্পর্কে দু’টি কথা

AUST যদি তার চরিত্র পরিবর্তন না করে তাহলে এই bank maths questions থেকে প্রচুর পরিমানে কমন পড়ার সম্ভাবনা রয়েছে। তবে একটা কথা অবশ্যই স্মরণে রাখবেন যে, এই bank maths questions গুলো আপনাকে হাতে-কলমে প্রাকটিস করতে হবে। কারণ, আপনি bank maths questions গুলো শুধু দেখে গেলেন আর উত্তর মুখস্ত করে রাখলেন কিন্তু পরীক্ষাতে যদি সংখ্যা পরিবর্তন করে দেয় তাহলে আপনি ধরা খাবেন। তাই যদি ধরা খেতে না চান তাহলে bank maths questions গুলো অন্তত একবার হলেও নিজে করুন।

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## bank maths questions and solutions 1 – 10

01.A garden of 100 m length and 60m width has a walkway of 2 m width on every side. What is the area of the garden, in square meter, excluding the walkway?

(a) 5684

(b) 6000

(c) 5376

(d) 5123

Solution:

Area of the garden excluding walkway = {(100-2×2) × (60-2×2)}= 96×56=5376m2

02.If a>b>l, then which of the following is true?

(a) (a-b)<0

(b) a2<ab

(c) (b+a)>2a

(d) a2>b2

Solution:

Let,

a = 3 & b=2

Option a) a2> b2 = (3)2> (2)2 = 9 > 4 True

Option b) a2 < ab = (3)2 < 3 x 2 =9<6 false

Option c) a – b<0= 3-2<0 = 1< 0 false

Option d) b +a > 2a = 2+3> 2 x 3 = 5 > 6 false

03.When 6 gallons of gasoline are put into a car, the indicator goes from 1/4 to 5/8. What is the total capacity of the gasoline tank?

(a) 12

(b) 14

(c) 16

(d) 18

Solution:

(5/8 – ¼) = 3/8 means 6 gallons

So, Total capacity = 6×8/3 = 16 gallons

04.A square carpet with an area of 169 cm2 must have 2 cm cut off one of its edges in order to be a perfect fit for a rectangular room. What is the area (in cm) of this rectangular room!

(a) 117

(b) 143

(C) 145

(d) 165

Solution:

Let, the carpet length = x

x2 = 169

x = 13

width of the room = (13-2) cm = 11 cm

area of the room = (13×11)2 = 143 cm2

05.A 10% monthly salary increase resulted in a Tk.9000 per year increase in salary for an employee. What was his monthly salary before the increase?

(a) Tk.7500

(b) Tk.8500

(c) Tk.5000

(d) Tk.9500

Solution:

Yearly increase = 9000 tk

Monthly increase = 9000/12 = 750 tk

10% of Salary is = 750 tk

100% of Salary is = (750×100)/10 = 7500 tk

06.The ratio between the perimeter and the breadth of a rectangular is 5:1. If the area of the rectangle is 216 cm2, what is the length of the rectangle?

(a) 16 cm

(b) 18 cm

(c) 20 cm

(d) 22 cm

Solution:

Let,

Length and breadth of the rectangle= x, y

So, area = xy

Perimeter = 2(x+y)

ATQ,

2(x+y)/y = 5

Or, 2x + 2y = 5y

Or, 2x = 3y

Or, y = 2x/3

Now,

xy = 216

Or, x  ×  2x/3  = 216

Or, 2x2 = 648

Or, x2 = 324

Or, x = 18

07.If for integer x, 5<x<10 and y=x+5, what is the greatest possible value of x+y?

(a) 32

(b) 22

(c) 23

(d) 27

Solution:

Given,

5 < x < 10 and y =x+5

Possible value of x = 6, 7, 8, 9

When x =9,

y =9+5 = 14

Now,

x + y = 9 + 14 = 23

08.In June a baseball team that played 60 games had won 30% of its games played. After a phenomenal winning streak this team raised its average to 50% How many games must the team have won in a row to attain this average?

(a) 30

(b) 45

(c) 20

(d) 24

Solution:

Now,
30% of 60+ x = 50% of (60+x)
Or, 18+x = 30+0.5x

Or, x = 24

09. In a container, there are 2 green marbles and 2 red marbles. You randomly pick the marbles. What is the probability that both of them are green?

A.    1/2

B.     1/3

C.     ¼

D.    1/6

উত্তর:  D

Solution:

green ball = 2

Red ball = 2

From 4 balls, possibility of 2 green = 4C2 = 6

From 2 balls, possibility of 1 green = 2C2 = 1.

From rest 2 balls, possibility of being green = 2C2=1

Possibility of 2 green = (2C2 x 2C2)/4C2= (1×1)/6= 1/6

10. To represent a family budget on a circle graph, how many degrees of the circle should be used to represent an item that is 20% of the total budget?

(a) 76°

(b) 72o

(c) 60°

(d) 20°

উত্তর:  72o

Solution:

Total circle = 360°

20% used 20% of 360° = (20/100) × 360° = 72°

## bank maths questions and solutions 11 – 20

11. A boat sailing against a stream of river tanks 6 hours to travel 24tm, while sailing with the stream it takes 4 hours to travel the same distance. What is the speed of the stream?

A.    2.5 km/hr

B.     1.5 km/hr

C.     1 km/hr

D.    0.5 km/hr

উত্তর:  1 km/hr

Solution:

Let,

Speed of stream =y &

Speed of boat = x

ATQ,

x-y= 24/6 = 4— (i)

x+y = 24/4 = 6 ——– (ii).

From,

(ii) – (i),

x+y-x+y = 6-4

Or, 2y = 2

Or, y = 1

12. A milkman purchases the milk at Tk. x per liter and sells it Tk. 2x per liter still he mixes 2 liters water with every 6 liters of pure milk. What is the profit percentage?

A.    116%

B.     166.66%

C.     60%

D.    100%

উত্তর:  166.66%

Solution:

Let,

He purchases 6liters milk.

So, cost of 6 liters = 6x tk.

After mixing 2 liters waters, he sells , (6+2)= 8 liters

Now, selling price of 8 liters = 8 × 2x = 16x tk.

Profit = 16x – 6x = 10x tk.

Profit percentage = (10x/6x) × 100 = 166.66%

13. A man could buy a certain number of notebooks for Tk. 300. If each notebook cost is Tk. 5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?

A.    15

B.     20

C.     10

D.    ৪

উত্তর:  10

Solution:

Let,

Cost of 1 Note book = x tk.

ATQ,

300/x  = {300/(x+5)} + 10

Or, (300/x) – 300/(x+5)  =  10

Or, (300x+1500-300x)/{x(x+5)} = 10

Or, x(x+5)10 = 1500

Or, x2+5x-150 = 0

Or, (x+15)(x-10) =0

Or, x≠ -15, x=10

14. Two-fifth of one-fourth of three seventh of a number is 15. What is the half of the number?

A.    75

B.     157

C.     175

D.    57

উত্তর:  175

Solution:

Let,

The number = x

ATQ,

2/5 × ¼ × 3/7 × x =15

Or, 16x/ 140 = 15

Or, x = 350

½ of 350 =175

15. Length of a train is 170 meters and speed of train is 63 km/hour. This train can pass a bridge in 30 seconds, then find the length of the bridge.

A.    355m

B.     325m

C.     365m

D.    312m

উত্তর:  355m

Solution:

Let,

Length of bridge = x m

ATQ,

63000/(60×80) = (170x+x)/30

Or, x+170 = 105 × 5

Or, x =525- 170

Or, x = 355

16. A water tank has two taps (Tap-1 and Tap 2). Tap-1 can fill a tank in 8 hours and Tap-2 can empty the tank in 16 hours. How long will they fill the tank if both taps are opened simultaneously but Tap-2 is closed after 8 hours?

10

12

14

16

উত্তর: 12

Solution:

Tap-1, fills in 1 hr =  1/8

Tap-2, empties in 1 hr = 1/16

When both taps are open, the tank fills in 1 hr = (1/8 – 1/16) = 1/16

In 8 hrs, the tank fills =  1/16 ×৪ = ½

Remaining = 1 – ½ = ½

½ is filled by only Tap 1

1/8 is filled by Tap-1 in 1 hr

So, ½ is filled by = (1×8)/2= 4 hr

Total time = 8+4 = 12 hr

17. A cylindrical rod of iron, whose height is equal to its radius, is melted and cast into spherical balls whose radius is half the radius of the rod. Find the number of balls.

A.    3

B.     4

C.     5

D.    6

উত্তর: 6

Solution:

Volume of cylinder = πr2h [Here h = r]

= πr2×r = πr3

Volume of sphere = 4/3 πr3  [Here r = r/2)

=(4/3) π× (r/2)3 = (πr3)/6

Number of balls = πr3/( πr3/6)= 6

18. Rahim borrowed Tk. 800 at 6% per annum and Karim borrowed Tk. 600 at 10% per annum. After how much time, will they both have equal debts?

A.    (50/3)×yr

B.     (83/3)×yr

C.     (44/3)×yr

D.    (20/3)×yr

উত্তর:  (50/3)×yr

Solution:

Let,

After x years their debts will be equal.

ATQ,

{800 × (6 × x)/ 100}+800 = {600 × (10 × x)/ 100}+600

⇒ 48x + 800 = 60x + 600

⇒ 60x – 48x = 800 – 600

⇒12x = 200

⇒ x = 50/3

19. The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?

A.    270

B.     1270

C.     350

D.    720

উত্তর:  270

Solution:

Let,

Smaller number = x,

difference =1365

So, the larger number = (x +1365)

ATQ,

6x +15 = x+ 1365

Or, 5x = 1350

Or, x= 270

20. The product of two positive numbers is p. If each of the number is increased by 2, the new product is how much greater than twice the sum of the two original number?

(a) p times

(b) 2p times

(c) (p + 4) times

(d) (2p + 3) times

উত্তর:  (p + 4) times

Solution:

Let,

One number is = x; other = y

xy = P —– (i)

(x + 2) (y + 2) = xy + 2y + 2x + y

xy + 2 (x + y) + 4 = xy + 4 + 2(x + y)

= P + 4 + 2(x + y)

The new result is (P+4) greater.

## bank maths questions and solutions 21 – 30

21. A and B together can do a piece of work in 40 days. A having worked for 20 days, finishes the remaining work alone in 60 days. In how many days shall B finish the whole work alone?

60 days

70 days

80 days

90 days

উত্তর:  C

Solution:

Let, A’s 1 day’s work = x and B’s 1 days work =y

Then,

x + y = 1/40 ——(1)

20x + 60y = 1 —-(2)

From (2) – (1)×20,

20x  + 60y – 20x -20y = 1 – ½

Or, 40y = ½

Or, y = 1/80

Therefore B’s 1 day work = 1/80

Hence, B alone finishes the work in 80 days

22. A jar contains white, red and green marbles in the ratios 2:3:5. Six more green marbles are added to the jars, and then the ratio becomes 2 : 3:7. How many white marbles are there in the jar?

A.    5

B.     6

C.     9

D.    10

উত্তর: 6

Solution:

Ratio of W : R : G= 2: 3:5।

If 6 Green is added, Ratio becomes W: R:G = 2: 3:7

Difference of ratio for 6 marbles = 7 – 5 = 2

For 1 ratio = 3 marbles

White marbles = 2×3 = 6

23. The length of a rectangular plot is 3 folds its width. Half the area of the plot is covered by a playground whose area is 363 square meter. What is the length of the plot?

A.    18.50m

B.     13.61m

C.     17.21m

D.    15.51m

উত্তর:  None

Solution:

Let, width = x

.:. The length of the plot = 3x

ATL,

x × 3x = 363 × 2

⇒3×2 = 363 × 2

⇒ x = 15.56

The length of the plot = 3×15.56 = 46.67 m

24. A box contains 10 electric bulbs from which 2 bulbs are defective. Two bulbs are chosen at random. What is the probability that one of them is defective?

A.    3/10

B.     16/45

C.     25/68

D.    8/33

=x 363×2

উত্তর:  16/45

Solution:

Defective 2; Normal ৪

Probability that one of them is defective will be,

= (8C1×2C2)/10C2

= (8×2)/45

= 16/45

25. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 6 hours. The number of hours taken by C alone to fill the tank is:

(a) 8 hours

(b) 10 hours

(c) 14 hours

(d) 18 hours

উত্তর:  18 hours

Solution:

A + B+C fill the tank in 6 hrs

A+B+C fill in 2 hrs = 2/6 = 1/3

Remaining = 1- 1/3 = 2/3

In 6 hrs A + B fill 2/3

In 1 hr A + B fill 2/3 × 1/6 = 1/9

Now C alone fill in 1 hr = 1/6 – 1/9 = 1/18

So, C needs 18 hrs to fill the tank.

26. If x=7 – 4√3 then find the value of x+1/x?

A.    3√3

B.     8√3

C.     14

D.    14 + 8√3

উত্তর:  14

Solution:

x =7 – 4√3

1/x = 1/(7 – 4√3) = (7 + 4√3)/ (7 – 4√3)( 7 + 4√3) = (7 + 4√3)/49-48 =(7 + 4√3)

x+1/x = 7 – 4√3 + 7 + 4√3 = 14

27. An employer pays 3 workers X, Y and Z a total of Tk. 36,600 a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. How much does X make a week?

A.    9,000

B.     12,000

C.     10,800

D.    11,700

উত্তর:  12,000

Solution:

X= 125% of y = 125y/100 = 5y/4

Or, y = 4x/5

Again,

X= 80% of z = 80z/100 = 4z/5

Or, z= 5x/4

X:y:z = x:4x/5:5x/4 = 20:16:25

Sum of ratio = 20+16+25=61

So, x makes a week = 20/61 × 36600 = 20×600=12000

28. The volume of a rectangular solid is to be increased by 50% without altering its base. To what extent the height of the solid must be changed.

A.    50%

B.     40%

C.     30%

D.    20%

উত্তর:  50%

Solution:

Let,

Volume = LBH

ATC,

LBH + 50% of LBH

=LBH + LBH/2

Let, H is to bbe increased by x%

So,

LB(H+Hx/100) = LBH + LBH/2

Or, LBH + LBHx/100 = LBH + LBH/2

Or, LBHx/100 = LBH/2

Or, x/100= ½

Or, x = 50%

29. If 892is added to the square of a number, the answer so obtained is 16202. What is the 1/26 of that number?

A.    5.65

B.     2.70

C.     3.50

D.    6.66

উত্তর:  3.50

Solution:

ATQ,

(89)2 + x2 = 16202

Or, x2 = 16202 – (89)2= 16202 – 7921 = 8281

.::x=√(8281) = ±91

Now, 1/26 of 91 = 3.50

30. A manufacturer sells three products i.e. A, B and C. Product A costs 200 and sells for 250, Product B costs 150 and sells for 180, Product C costs 100 and sells for 110. On which product, he has maximum percentage of profit?

A.    B Only .

B.     A and B both

C.     A Only

D.    C Only

Solution:

Profit from A = 250-200=50tk

Percentage = (50×100)/200=25%

Profit from  B= 180-150=30tk

Percentage = (30×100)/150= 20%

Profit from C= 110-100=10tk

Percentage= (10×100)/100=10%

## bank maths questions and solutions 31 – 40

31. The average of 6 numbers is 25. If 3 more numbers, with an average of 22 are added to these numbers, what will be the average of the combined 9 numbers?

A.    20

B.     24

C.     28

D.    32

Solution:

The average of 6 numbers is 25

The Total of 6 numbers is =25×6=150

The average of 3 numbers is 22

The Total of 3 numbers is =22×3=66

The Total of (6+3)=9 numbers is =(150+66)=216

The average of 9 numbers is=216/9=24

32. In a club 50% of the male voters and 80% of the female voters voted for candidate A. If candidate A received 70% of the total votes, what is the ratio of male to female voters?

A.    1/5

B.     ¼

C.     ½

D.    1/3

Solution:

Male voter = x

Female voter = y

50% of x + 80% of y = 70% of (x+y)

50x/100 + 80y/100 = 70(x+y)/100

50x + 80y = 70x + 70y

80y – 70y= 70x – 50x

10y = 20x

x/y = 10/20 = ½

33. If x+y>5 and x – y>3, then which of the following gives all possible values of x and only possible values of x?

A.    x>4

B.     x>3

C.     x > 2

D.    x<4

34. The interest charged on a loan is p dollars per \$1,000 for the first month and q dollars per \$1,000 for each month after the first month. How much interest will be charged during the first three months on a loan of \$10,000?

A.    10p+20q

B.     30q

C.     30p

D.    20p+10q

Solution:

Interest = 1st month + 2nd month + 3rd month

= p×(10000/1000) + q×(10000/1000)  + q×(10000/1000)

=10p +10q + 10q

= 10p + 20q

35. A box contains 12 poles and 7 pieces of net. Each piece of net weighs 0.2 gm; each pole weighs 1.1 gm. The box and its contents together weigh 16.25 gm. How much does the empty box weigh?

A.    1.25 gm

B.     1.65 gm

C.     2.25 gm

D.    2.65 gm

Solution:

Weight of 7 nets = (7×0.2)gm =1.4gm

Weight of 12 poles = (12×1.1)gm = 13.2gm

Total weight of net and pole = (1.4+13.2)gm = 14.6gm

Box weight is = (16.25 – 14.6) = 1.65gm

36. Triangle ABC has the following vertices: A(1,0), B(5,0) and C(3, 4). Which of the following is true?

A.    CA = CB

B.     AB = AC

C.     AC < BC

D.    AB = BC

উত্তর: CA = CB

Solution:

Distance of  (x1,y1) & (x2,y2) = √{(x1 – x2)2 + (y1 – y2)2}

AB/BA = √{(1 – 5)2 + (0 – 0)2 }= √(-4)2 = √16 = 4

BC/CB = √{(5 – 3)2 + (0 – 4)2 }= √22 + 16 = √20 = 2√5

AC/CA=√{(1-3)2 + (0 – 4)2 }= √4 + 16 =√20 = 2√5

37. Increasing the original price of an item by 10%, then decreasing by 20% and then again increasing the price by 10% is equivalent:

A.    4.4% increase

B.     3.2% decrease

C.     3.5% decrease

D.    None of these

উত্তর: 3.2% decrease

Solution:

Let,

Selling price = 100

After 10% increase = (100+10)=110

After 20% decrease = (110 – 20% of 110) = 88

After 10% increase = (88 + 10% of 88) = 96.8

Final decrease = (100-96.8)=3.2%

38. A student loses 1 mark for every wrong answer and scores 2 marks for every correct answer. If he answers all the 60 questions in an exam and scores 39 marks, how many of them were correct?

A.    33

B.     31

C.     27

D.    37

উত্তর: 33

Solution:

Let,

Number of wrong answers = x

ATQ,

2(60-x) -x = 39

⇒120 -2x-x = 39

⇒-3x = 39-120

⇒-3x = -81

⇒x = 27

correct answer = (60 – 27) = 33

39. The triangular base of a prism is a right triangle of sides a and b = 2a. The height h of the prism is equal to 10 mm and its volume is equal to 40 mms, what will be the lengths of the sides a and b of the triangle?

A.    2 mm and 3 mm

B.     1 mm and 4 mm

C.     2 mm and 2 mm

D.    2 mm and 4 mm

উত্তর: 2 mm and 4 mm

Solution:

½ × abc = 40

Or, abc = 80

Or, a × 2a × 10 = 80

Or, 20a2 = 80

Or, a2 = 2

Or, a = 2

And b = 2a = 2×2 = 4

40. The sum of principal and simple interest of a certain amount of money would be Tk. 460 after 3 years from now and Tk. 500 after 5 years from now. What is the total interest rate?

A.    5%

B.     12%

C.     15%

D.    20%

উত্তর: 5%

Solution:

(5 – 3) yr = 2 yrs interest = (500 – 460) = 40 tk

1 year interest = 40/2 = 20 tk.

3 year interest = (20 × 3) = 60 tk

Principal amount= (460 – 60) = 400 tk

Interest rate = 60/(400×3) = 0.05 = 5%

## bank maths questions and solutions 41 – 50

41. A wheel rotates 10 times per minutes and moves 20m during each rotation. How many feet does the wheel move in 1 hour?

A.    10,000

B.     12,000

C.     18,000

D.    20,000

উত্তর: None

Solution:

In 1 min the wheel passes = (20 × 10) = 200m

In 60 min the wheel passes =  (200 x 60) = 12,000m

We know,

1m =3.28 feet

.: 12,000m=(3.28 × 12,000) = 39360 feet

42. If x and y are consecutive positive integers, which of the following must be an even integer?

A.    X

B.     y

C.     xy/2

D.    xy

উত্তর: xy

Solution:

As X and Y are consecutive positive integers, one will be even and the other odd.

odd × even= even

43. The ratio between the perimeter and the breadth of a rectangular is 5:1. If the. area of the rectangle is 216cm, what is the length of the rectangle?

A.    16cm

B.     18cm

C.     20cm

D.    22cm

উত্তর: 18cm

Solution:

Let,

Length and breadth of the rectangle= x, y

So, area = xy

Perimeter = 2(x+y)

ATQ,

2(x+y)/y = 5

Or, 2x + 2y = 5y

Or, 2x = 3y

Or, y = 2x/3

Now,

xy = 216

Or, x  ×  2x/3  = 216

Or, 2x2 = 648

Or, x2 = 324

Or, x = 18

44. jf (x + y) > 5 and (x – y) > 3, then which of the following gives all and only possible value of x?

A.    x<3

B.     x> 3

C.     x> 4

D.    x < 5

উত্তর: x> 4

Solution:

Given,

(x + y) > 5 —-(1)

(x – y) > 3 —–(2)

(1)+(2),

2x >8

Or, x>4

45. Three boys have marbles in the ratio of 19: 5: 3. If the boy with the least number has 9 marbles, how many marbles does the boy with the highest number have?

A.    57

B.     15

C.     76

D.    38

উত্তর: 57

Solution:

Smaller ratio 3 = 9

So, Smaller ratio 1 = 9/3 = 3

Now,

Highest ratio 19 = 19×3 = 57

46. The area of a rectangle R with width 4 ft is equal to the area of a square S, which has a perimeter of 24 ft, the perimeter of the rectangle R, in feet, is

A.    9

B.     16

C.     24

D.    26

উত্তর: 26

Solution:

Given,

Perimeter of the square = 24

So, side of the square = 24/4=6

Area = 62 = 36

Let,

Length of the rectangle = x

ATQ,

4x = 36

Or, x= 9

So, perimeter of the rectangle = 2(9+4) = 26

47. In a class of 120 students, 70 percent can speak only Bengali and the rest can speak English. If 25 percent of those in the class who can speak English can also speak Bengali, how many of the students in the class can speak Bengali?

A.    39

B.     48

C.     84

D.    93

উত্তর: 93

Solution:

Only speak bangla = 120 × 70/100 = 84

Speak English = 120× 30/100 = 36

Now,

25% of 36 = 36× 25/100 =9 can also speak bangla

So, total bangla speaking student =(84 +9) = 93

48. A lamp is manufactured to sell for \$35.00, which yields a profit of 25% of cost. If the profit is to be reduced to 15% of cost, what will be the new retail price of the lamp?

A.    \$31.50

B.     \$28.00

C.     \$21.00

D.    \$32.20

উত্তর: \$32.20

Solution:

In  25% profit,

If selling price 125 then cost = 100

So, when selling price 35 then cost = (100×35)/125 = 28

In 15% profit,

If cost is 100 then selling price = 115

So, when cost is 28, then selling price = (115×28)/100 = 32.20

49. In triangle ABC, AB = AC. All of the following statements are true except

A.    AB < AC + BC

B.     AC< AB + BC

C.     BC+ AC> AB + BC

D.    AC+ BC= AB + BC

উত্তর: BC+ AC> AB + BC

Solution:

Given,

AB = AC

Or, BC + AB = BC + AC [Adding BC to both sides]

So, BC + AC > AB + BC can’t be.

50. There are 15 balls in a box: 8 balls are green, 4 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?

A.    3/15

B.     4/15

C.     3/13

D.    4/13

উত্তর: 3/13

Solution:

green balls = (8 – 1) = 7

blue balls = (4 – 1) = 3

white balls = 3

possibility of getting a blue ball = 3/(7+3+3) = 3/13

## bank maths questions and solutions 51 – 60

51. A short distance athlete has taken 60 seconds to cover 100 meters. If he makes 30 steps in 9 seconds, how many steps has he taken in that time?

A.    130

B.     170

C.     173

D.    None of these

উত্তর: None of these

Solution:

9 sec = 30 steps

60 sec = (30×60)/9= 200 steps

52. Three angles of a triangle are in proportion 5: 6:7. Then what is the difference in degrees between the biggest and the smallest angles?

A.    10°

B.     20°

C.     25°

D.    30°

উত্তর: 20°

Solution:

Sum of 3 angles of a triangle = 180°

Sum of ratio = 5+6+7 = 18

So, the larger angle = 180° × 7/18 = 70°

And, the smaller angle = 180° × 5/18 = 50°

Difference = 70° – 50° = 20°

53. A farmer has two rectangular fields. The larger field has twice the length and four times the width of the smaller field. If the smaller field has area K, then the area of the larger field is greater than the area of the smaller field by what amount?

A.    2K

B.     5K

C.     6K

D.    7K

উত্তর: 7K

Solution:

Let,

Length of smaller field = x

So, length of larger field = 2x

Again,

Width of smaller field = y

So, width of larger filed = 4y

Area of smaller field = xy = K

Area of larger field = 2x × 4y = 8xy = 8K

Difference = 8K – K = 7K

54. In a club 50% of the male voters and 80% of the female voters voted for candidate A. If candidate A received 70% of the total votes, what ‘is the ratio of male to female voters?

A.    1/3

B.     ½

C.     ¼

D.    ¾

Solution:

Let, total member of the club = 100 and male member =x

Female member = (100-x)

Now,

x×50% + (100-x)80% = 70×100%

5x +(100-x)8 = 70×10

5x + 800 – 8x = 700

3x = 100

X = 33.33

Now, female: Male = 33.33 : (100-33.33) = 1:2

55. Four liters of milk are to be poured into a 2 liter bottle and a 4 liter bottle. If each bottle is to be filled to the same fraction of its capacity, how many liters of milk should be poured into the 4 liter bottle?

A.    7/3

B.     2/3

C.     8/3

D.    4/3

Solution:

Let, milk in 4 litter bottle is x litter

So, milk in 2 litter bottle is (4-x) litter

x/4 = (4-x)/2

x = 8-2x

x = 8/3

56. One dozen eggs and ten pounds of apples are currently of the same price. If the price of a dozen eggs rises by 10% and that of apples rises by 2%, how much more will it cost to buy a dozen of eggs and ten pounds of apples?

A.    2%

B.     6%

C.     10%

D.    12%

Solution:

Say, Cost of eggs = Cost of apples = 100

Total = 200

New egg cost = 110

New apple cost = 102

New total = 110 + 102 = 212

Percentage increase ={(212−200)/200}×100= 6%

57. An iron rod that weighs 24 kg is cut into two pieces so that one of these pieces weighs 16 kg and is 34m long. If the weight of each piece is proportional to its length, how long is the other piece?

A.    11m

B.     17m

C.     34m

D.    68m

Solution:

16 kg rod = 34m

24 kg rod = (34×24)/16 = 51m

Length of the other part is = 51-34 = 17m

58. The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

A.    20%

B.     25%

C.     50%

D.    37.5%

Solution:

Let price of book = 100tk

Price of pen = 100+100×25% = 125 tk

Price of penholder = 100 + 100×50% = 150 tk

Difference is = 150 -125 = 25 tk

Percentage = (25×100)/125 = 20%

59. Three individuals contributed Tk 8,000 each toward the purchase of a computer. If they bought the computer on sale for Tk. 19500 plus 10% sales tax, how much money should be refunded to each individual?

A.    Tk. 650

B.     Tk. 850

C.     Tk.1,500

D.    Tk1,950

Solution:

Contribution of three person = 8000×3 = 24000 tk

Cost of the computer = 19500+19500×10% = 19500+1950 = 21450 tk

3 person get back = 24000 – 21450 = 2250 tk

1 person get back = 2250/3 = 850 tk

60. When a certain number is divided by 7, the remainder is 0. If the remainder is not 0 when the number is divided by 14, then the remainder must be

A.    7

B.     5

C.     3

D.    8

Solution:

If a number is divisible by 7, remainder will be 0. So, any number divisible by any multiple of 7 will leave remainder 7 or 0.

## bank maths questions and solutions 61 – 70

61. A mixture of 20 kg of sprit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%

A.    2

B.     4

C.     5

D.    6

Solution:

Water contains in mixture = 20×10% = 2 kg

Sprit in the mixture = 20-2 =18 kg

x litter water need to mix in the mixture.

So, (2+x)/18 = 25/75

(2+x)/18 = 1/3

6+3x = 18

x = 4

62. How much interest will Tk. 1,000 earn in one year at an annual interest rate of 20% if interest rate is compounded every 6 months?

A.    200

B.     205

C.     208

D.    210

Solution:

We know,

C= P(1+r/m)n×m

=1000{1+20/(100×2)}1×2

= 1000{1+1/10}2 = 1210

Interest = 1210-1000 = 210 tk

63. A garden of 100% length and 60m width has a walkway of 2m width on every side. What is the area of the garden, in square meter, excluding the walkway?

A.    5684

B.     6000

C.     5376

D.    5123

Solution:

Length of the garden excluding road = 100-2×2 =96m

Width of the garden excluding road = 60-2×2 =56m

Area garden excluding road = 96×56 =5376 sq. m

64. The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?

A.    12

B.     24

C.     26

D.    None of these

Solution:

ATQ,

A + B = 12 + B +C

A = 12 +C

That is, C is 12 years younger than A.

65. An article when sold at a gain of 5% yields Tk.15 more than when sold at a loss of 5%. Its cost price would be

A.    Tk. 100

B.     Tk. 150

C.     Tk. 200

D.    Tk. 250

Solution:

At 5% profit, selling price = 100+5=105 tk.

At 5% loss, selling price = 100-5= 95 tk.

Difference between selling price = 105-95=10 tk.

If difference 10, then cost = 100tk

If difference 1, then cost = 100/10 tk

If difference 15, then cost = (100×15)/10 tk = 150tk.

66. If ax = b, by = c, and cz = a, then the value of xyz is

(a) 0

(b) 1

(c) 1/abc

(d) abc

Solution:

Given,

ax = b

Or, (cz)x = b

Or, (by) z x = b

Or, (b) xyz = b1

Or, xyz = 1

67. For what value of x is 82x-4 =16x?

1. 2
2. 3
3. 4
4. 6

Solution:

Given,

82x-4 =16x

Or, 23(2x-4) = 24x

Or, 6x -12 = 4x

Or, 2x = 12

Or, x = 6

68. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

A.    13 days

B.     15 days

C.     10 days

D.    None of these

Solution:

Ratio of times taken by A and B = 100 : 130 = 10 : 13.

Suppose, B takes x days to do the work.

Then,

10 : 13 = 23 : x

Or, x = (23 x 13)/10

Or, x = 299/10

A’s 1 day’s work = 1/23

B’s 1 day’s work = 10/299

(A + B)’s 1 day’s work =(1/23 +10/299)= 23/299 =1/13

Therefore, A and B together can complete the work in 13 days.

69. The lengths of the sides of a triangle are in the ratio of 3 to 5 to 6. If the perimeter of the triangle is 70, what is the length of the longest side?

A.    10

B.     15

C.     25

D.    30

Solution:

3x+5x+6x=70

Or, 14x=70

Or, X=5

Length of the longest side= 5×6=30

70. If for integer x, 5 <x<10 and y = x + 5, what is the greatest possible value of x + y?

A.    32

B.     22

C.     23

D.    27

Solution:

Given,

5 < x < 10 and y =x+5

Possible value of x = 6, 7, 8, 9

When x =9,

y =9+5 = 14

Now,

x + y = 9 + 14 = 23

## bank maths questions and solutions 71 – 80

71. Square of a number plus two times the number equal 63. What is the number?

A.    7

B.     9

C.     –9

D.    ৪

Solution:

x2 + 2x = 63

x2 + 2x – 63 = 0

x2 + 9x – 7x – 63 = 0

x (x + 9) – 7 (x + 9) = 0

(x + 9) (x – 7) = 0

x = –9 and x = 7

72. If the perimeter of a certain rectangle is 76m and its area is 360m2, then what is the length of its shortest side?

A.    18

B.     15

C.     13

D.    10

Solution:

Let, length = x and width = y

Now, 2(x+y) = 76

x+y =38………(i)

xy = 360

x = 360/y……..(ii)

(i)=

360/y + y =38

360 + y2 = 38y

y2 -38y + 360 = 0

y2 -20y – 18y + 360 = 0

y(y -20) – 18(y – 20) = 0

(y -20) (y – 18) = 0

y= 20 and 18

Width = 18m

73. If x=1+ √2 and y =1-√2 find the value of (x2 + y2)

(a) 12

(b) 10

(c) ৪

(d) 6

Solution:

x2 + y2

=(1+ √2) 2 + (1-√2) 2

= 1 + 2√2 + 2 + 1 – 2√2 + 2

=6

74. If x and y are consecutive positive integers, which of the following must be an even integer?

A.    X

B.     Y

C.     xy/2

D.    xy

Solution:

As x & y are consecutive positive integers, one of them must be odd and the other even.

Now, Odd×Even= Even.

75. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM, if one travels directly north at 150 mph and the other travels directly west at 200 mph?

A.    50 miles

B.     100 miles

C.     500 miles

D.    700 miles

Solution:

Plane travels for 2 hours

1st one passes =150×2=300mile

2nd one passes =200×2=400mile

Distance between them

d2 = 3002 + 4002

Or, d = √(90000 + 160000) = √250000 = 500

76. A short distance athlete has taken 30 seconds to cover 100m. If he makes 30 steps in 9 seconds, now many steps he taken in that time?

A.    130

B.     170

C.     173

D.    None

Solution:

9 sec = 30 steps

60 sec = (30×60)/9= 200 steps

75. A car goes 15 km on a gallon of octane when it is driven at 50 km/h. When the car is driven at 60 km/h, it only goes 80% as far. How many gallons of octane are needed to travel 200 km if half the distance is traveled at 50 km/h and the rest at 60 km/h?

A.    15

B.     16.67

C.     10.60

D.    14

Solution:

At 50km/h

15 km needs 1 gallon

So, 100 km needs 100/15 gallon

At 60km/h,

It goes 80% far = 80% of 15 = 12 km

12 km needs 1 gallon

So, 100 km needs 100/12 gallon

So, (100+100) = 200 km needs

= (100/15 + 100/12) gallon

= (400+500)/60 gallon

= 900/60 gallon

= 15 gallon

76. A manufacturer sells three products i.e. A, B and C. Product A cost 200 and sells for 250, Product B cost 150 and sells for 180, Product C cost 100 and sells for 110. On which product, he has maximum percentage of profit?

A.    B only

B.     A and B both

C.     A only

D.    C only

Solution:

Profit from A = 250-200=50tk

Percentage = (50×100)/200=25%

Profit from  B= 180-150=30tk

Percentage = (30×100)/150= 20%

Profit from C= 110-100=10tk

Percentage= (10×100)/100=10%

77. A, B and C enter into partnership with investments in the ratio of 5:7: 8. If, at the end of the year A’s share of profit is Tk. 42,360, how much is the total profit?

A.    Tk. 169,440

B.     Tk. 183,000

C.     Tk. 196,700

D.    Tk. 168,440

Solution:

As the profit distributed according to the investment ratio the profit and investment ratio will be equal

Let, A’s profit = 5x tk

5x = 42360

x = 8472

B’s profit = 8472×7= 59304

C’s profit = 8472×8= 67776

Total profit = 43260+59304+67776=169440

78. One third of the faculty members of a department are female. Sixteen of the male teachers are unmarried while 60% of them are married. The total number of faculty members in the department is

A.    72

B.     60

C.     30

D.    90

Solution:

Let,

Total number = x

Number of female = 1/3 of x = x/3

Number of male = x-x/3 =  2x/3

Married male = 60% of 2x/3 = 2x/5

ATQ,

2x/3 – 2x/5 = 16

Or, 4x/15 = 16

Or, x = 60

79. A wholesaler sells goods to a retailer at a profit of 20%. The retailer sells to the customer, who pays 80% more than the cost of the wholesaler. What is the retailer’s profit?

A.    40%

B.     50%

C.     60%

D.    70%

Solution:

Let cost of wholesaler = 100tk

At 20% profit he sells = 120tk = the cost of retailer

Retailer sell it for 80% profit on cost of wholesaler

= 100 + 100×(80/100) = 180 tk

Profit of retailer = 180- 120 = 60 tk

Percentage = (60×100)/120 = 50%

80. If an integer y is subtracted from an integer x, and the result is greater than x, then y must be –

A.    Equal to x

B.     less than 0

C.     less than x

D.    greater than 0

Solution:

ATQ,

x-y>x

Or, -y > 0

Or, y < 0

## bank maths questions and solutions 81 – 90

81. A train went 300 km from City X to City Y at an average speed of 100 km/h. At what speed did it travel on the way back if its average speed for the whole trip was 120 km/h?

A.    120 km/h

B.     125 km/h

C.     130 km/h

D.    150 km/h

Solution:

Let,

Way back speed = x

ATQ,

2×x×100/(x+100) = 120

Or, 200x/(x+100) = 120

Or, 200x = 120x+12000

Or, 80x = 12000

Or, x= 150

82. If a, b and c are 3 consecutive integers and a >b>c, which of the following has the maximum value?

A.    b+(c/a)

B.     c+(a/b)

C.     c+(b/a)

D.    a+(b/c)

Solution:

As a is the greater number, adding a to any fraction of the given choice will have the maximum value.

83. Sam can mow a lawn in 20 min, while Mark takes 10 min longer to mow the same lawn. How long will they take to mow the lawn if they work together?

A.    12 min

B.     more than 15 min

C.     15 min

D.    14 min

Solution:

In 1 minute, Sam mows 1/20 of the lawn

In 1 minute, Mark mows 1/(20+10) = 1/30 of the lawn

(1/20 + 1/30) = 5/60=1/12 of the lawn takes 1 minute

So, whole(1) lawn takes 12 minutes

84. If two planes leave the same airport at 1:00 pm, how many km apart will they be at 3:00 pm, if one travels directly north at 150 km/h and the other travels directly west at 200 km/h?

A.    50km

B.     500km

C.     400km

D.    600km

Solution:

Difference of time = 3:00 pm – 1:00 pm = 2 hrs

First plane travels in 2 hrs = 2×150=300 km

Second plane travels in 2 hrs = 2×200=400 km

The directions of the planes forms a right angle triangle

So, the direct distance = √(3002 + 4002) = √250000=500 km

85. If an inspector rejects 0.08% of a product as defective, how many units of the product will he examined in order to reject 2?

A.    500

B.     1500

C.     2000

D.    2500

Solution:

0.08 product is rejected from = 100

So, 2 product is rejected from = (100 × 2 × 100)/0.08 = 2500

86. A two-digit number has 3 in its unit digit. The sum of its digits is one seventh of the number itself. What is the number?

A.    53

B.     63

C.     73

D.    83

Solution:

Let,

The number = 10x + 3

ATQ,

7(x + 3) = 10x + 3

⇒7x + 21 = 10x + 3

⇒21-3 = 10x – 7x

⇒3x = 18

⇒x= 6

The number = 10 × 6 + 3 = 63.

87. A trader market the price of an article 30% above the cost price and gave the buyer 10% discount on marked price, thereby gaining Tk. 340. The cost of the article is?

A.    3000

B.     2000

C.     1900

D.    1800

Solution:

88. The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by?

A.    62%

B.     42%

C.     82%

D.    None

Solution:

Let, length is = x so, area is = x2

40% increase in length = x+2x/5 =7x/5

30% increase in breadth = x+3x/10 =13x/10

Area = (7x/5)×( 13x/10) = 91x2/50

Increasing area = (91x2/50)- x2 = 41x2/50

Percentage = {(41x2/50) x2}×100 = (41/50)×100 = 82%

89. There boys have marbles in the ratio of 19:5:3. If the boy with the least number has 9 marbles, how many marbles does the boy with the highest number have?

A.    57

B.     15

C.     76

D.    38

Solution:

Smaller ratio 3 = 9

So, Smaller ratio 1 = 9/3 = 3

Now,

Highest ratio 19 = 19×3 = 57

90. A circular wheel 28 inches in diameter rotates the same number of inches per second as a circular wheel 35 inches in diameter. If the smaller wheel makes x revolutions per second, how many revolutions per minutes does the larger wheel make in terms of x?

A.    12x

B.     24x

C.     36x

D.    48x

Solution:

For smaller wheel,

Circumference = 2×π×28/2 = 28π

Revolve in 1 second = x times

Revolve in 60 seconds = 60x times

So, distance = 28π×60x

For larger wheel,

Circumference = 2×π×35/2 = 35π

Let,

Revolve per minute = n

So, distance = 35πn

Now,

28π×60x = 35πn

Or, n=(28π × 60x)/35π

Or, n= 48x

## bank maths questions and solutions 91 – 100

91. Of two groups of tourists, each has 60 people. If three-fourth (i.e. 75%) of the first group and two-third of the second group board buses to travel to a museum. How many more people of the first group board buses than that of the second group?

A.    3

B.     5

C.     10

D.    15

Solution:

¾ of first group = ¾ of 60 = 45

2/3 of 2nd group = 2/3 of 60 = 40

Difference = 45-40 = 5

92. Six consecutive whole numbers are given. The sum of the first three numbers is 27. What is the sum of the last three numbers?

A.    30

B.     32

C.     36

D.    38

Solution:

Let,

Numbers are n, n+1, n+2

ATQ,

n+n+1+n+2 =27
Or, 3n+3=27
Or, 3n=24
Or, n=8
So, the numbers are-8,9,10

Now, the last 3 consecutive numbers are 11,12,13

Sum of them 11+12+13 =36

93. If the length of each of the sides of three square garden’s plots is increased by 50 percent, by what percent is the sum of the areas of the three plots increased?

A.    125%

B.     150%

C.     200%

D.    375%

Solution:

Let, the length of each side of the garden = 100

Area = 1002 = 10000

Area of 3 square = 3×10000 = 30000

50% increase of length = 100+100×50/100 = 150

Area = 1502 = 22500

Area of 3 square = 3×22500 = 67500

Increasing area = 67500-30000 =37500

Percentage = (37500×100)/30000=125%

94. Karim has 40% more stamps than Rahim if he gives 45 of his stumps to Rahim, then Rahim will have 10% more stamps than Karim. How many stamps did Karim begin with?

A.    175

B.     200

C.     220

D.    245

Solution:

Let,

Rahim has = x stamps

So Karim has = 140% of x = 1.4x

ATQ,

110% of (1.4x-45) = x+45

Or, {11(1.4x – 45)/10} = x + 45

or, 15.4x-495 = 10x+450

or, 5.4x = 945

Or, x= 175

So, Karim has 175+ 40% of 175 = 175+70 = 245

95. P & Q start a business with initial investments in the ratio of 13:8. Their corresponding profits are in the ratio of 7:5. If P invested his money for 7 months, find the time period for what Q invested his money.

A.    8 months

B.     9 months

C.     10 months

D.    11 months

Solution:

Let,

Q invested for x months

ATQ,

(13×7) : (8×x) = 7:5

Or, 91/8x = 7/5

Or, 8x = 91×5/7

Or, x = 65/8=8.125 =8

96. Compound interest on a certain sum for 2 years at 10% per annum is Tk.420. What would be the simple interest at the same rate and for the same time?

A.    Tk100

B.     Tk.200

C.     Tk.300

D.    Tk.400

Solution:

Let,

Principal =P

ATQ,

P × (|1+ 10/100)2 –P = 420

Or, P(11/10)2 –P = 420

Or, P(1.1)2 – P = 420

Or, 1.21P – P = 420

Or, P(1.21 – 1) = 420

Or, 0.21P = 420

Or, P = 2000

Simple interest = 2000 × 2 × 10/100 = 400

97. Ravi leaves home for stadium which is 12 km from his house. After the stadium, he goes to his club which is 7 km from his stadium. If his home, stadium and club all fall in a line, then what is the minimum distance he has to travel to get back home?

A.    19 km

B.     7 km

C.     5 km

D.    12 km

Solution:

His last destination was club. This club may be either side of stadium and in a straight line.  So, minimum distance = 12-7 = 5km

98. If a man cycles at 10 km/hr, then he arrives at a certain place at 1 pm. If he cycles at 15 km/hr, arrive at the same place at 11 am. At what speed must he cycles to go there at noon?

A.    11 km/hr

B.     12 km/hr

C.     13 km/hr

D.    14 km/hr

Solution:

Let,

distance = x

Time difference(Same Day) = 1 PM. – 11 AM. = 2 hours.

ATQ,

x/10 – x/15 = 2

Or, x/30 = 2

Or, x = 60

30

.:.x = 60

When speed is 10km/hr then time taken = 60 ÷10 = 6 hours.

So, at 10km/hr, his starting time was = 1PM. – 6 hours = 7 AM(Same Day)

So, to reach at noon or 12 P.M, total time needed = 12 P.M. –7 A.M = 5hours.

Thus, speed = 60 ÷ 5 = 12km/hr.

99. Three measuring rods are 64 cm. 80 cm and 96 cm length. What is the least of cloth that can measure exact number of rods using any one of these rods?

A.    9.60 m

B.     8.0 m

C.     9.60 cm

D.    96 m

Solution:

L.C.M of 64 80 and 96 = 960 cm

100 cm = 1 m

or 960 cm = 9.6 m

7. Which of the following equals – (√2 -√8)(2√2 +√8)?

-2√2

-4

4√2

-8

Solution:

(√2 -√8)(2√2 +√8)

=(√2 -2√2)(2√2 +2√2)

=4√2(√2 -2√2)

=4√2.√2(1 – 2)

= – 4√2.√2

= – 8

100. A tank can be filled by a tap in 20 minutes and by another tap in 60 minutes both the taps are kept open for 10 minutes and then the first tap is shut off. After this, the tank will completely filled in what time?

A.    10 min

B.     15 min

C.     20 min

D.    25 min

Solution:

In 1 min both taps fill = 1/20 + 1/60 = 4/60 = 1/15

So, in 10 minutes taps fill = 10 × 1/15 = 2/3

Remaining part = 1 – 2/3 = 1/3

After shutting off 1st tap,

2nd tap fills 1/3 part in 60 × 1/3 minutes = 20 minutes

## bank maths questions and solutions 100 – 118

101. A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is

A.    7/19

B.     6/19

C.     5/19

D.    3/19

Solution:

Here, Total bulbs = 20

defective bulbs = 4

so, non defective bulbs = 20-4 = 16

Probability = 16C2 / 20C2 = (16 × 15)/2 ÷ (20 × 19)/2 = 120/190 = 12/19

.:. at least 1 defective = 1 – 12/19 = 7/19

102. There is a rectangular parking lot with a length of 2x and a wide of x. What is the ratio of the perimeter of the parking lot to the area of the parking lot, in terms of x ?

A.    2/x

B.     3/x

C.     4/x

D.    5/x

Solution:

Perimeter =2(2x+x) = 6x

Area = 2x × x = 2x2

Ratio = 6x:2x2 = 3:x = 3/x

103. The ratio of income of A to that of B is 7:5 and expenditure of A to that B is 3 : 2. If at the end of the year, each saves Tk. 500, find the income of A?

A.    Tk. 2500

B.     Tk. 300

C.     Tk. 3200

D.    Tk. 3500

Solution:

Let, income of A and B = 7x and 5x

And expenditure = 3y and 2y respectively

ATQ,

7x-3y = 500 —– (i)

5x-2y = 500 —– (ii)

From (ii) × 3 – (i) × 2,

15x – 6y -14x + 6y = 1500 – 1000

Or, x = 500

So, income of A = 7×500 =Tk. 3500

104. An empty bucket (Foto) being filled with paint at a constant rate takes 6 min to be filled 7/10 of its capacity. How much more time will it take to fill the bucket to full capacity

A.    18/7

B.     6/19

C.     20/14

D.    18/14

Solution:

7/10 tool 6 m

So, 1 took 6 × 7/10 m

So, 3/10 took 6 × 7/10 × 3/10 m = 18/7 m

105. In distributing milk at a summer camp it is found that a quart of milk will fill either 3 large glass tumblers or 5 small glass tumblers. How many small glass tumblers can be filled with one large glass tumbler?

A.    11/5

B.     7/5

C.     5/3

D.    7/3

Solution:

3 large = 5 small

So, 1 large = 5/3 small

106. A bank offers 5% interest compounded half yearly. A customer deposits Tk.1600 each on 1st January and 1st. July of a year. At the end of the year the amount he would have gained by the way of interest is

A.    Tk. 121

B.     Tk. 122

C.     Tk. 123

D.    Tk. 124

Solution :

Total amount = 1600(1+5/2 %)2  + 1600(1+5/2 %)

=1600{1+ 5/(2×100)}2 + 1600{1+ 5/(2×100)}

= 1600(1+1/40)2 +1600(1+1/40)

= 1600 × 41/40 × 41/40 + 1600 × 41/40

= 1600 × 41/40 (41/40 + 1)

= 1600 × 41/40 × 81/40 =3321

Gain = 3321 – (1600+1600) = 121

107. A box is made in the form of a cube. If a second cubical box inside dimensions three times those of the first box, how many times as much does the second box contain?

A.    6

B.     9

C.     12

D.    27

Solution:

Let,

one side of first cube = a

So, Volume of first cube = a3

ATQ,

One side of the 2nd cube = (3a)3 = 27a3

Times = 27a3 / a3  = 27

108. A can do a job in 24 days, B in 9 days and C in 12 days. B and C together start the work but leave after 3 days. How much time was taken A to complete remaining work?

A.    7 days

B.     9 days

C.     10 days

D.    12 days

Solution:

B+C do in 1 day = 1/9 + 1/12 = 7/36

B+C do in 3 days = 3 × 7/36 = 7/12

Remaining = 1 – 7/12 = 5/12

A does 1 part in 24 days

So, A does 5/12 part in 24 × 5/12 = 10 days

109. In a group of 15, 7 can speak Spanish 8 can speak French and 3 can speak neither. What fraction of the group can speak both French and Spanish?

A.    1/5

B.     4/15

C.     1/3

D.    7/15

Solution:

n(SUF) = n(S) + n(F) –n(S∩F) + none

Or, 15 = 7 + 8 – n(S∩F) + 3

Or, n(S∩F) = 3

The fraction = 3/15 = 1/5

110. A, B and C enter into partnership by making investments in the ratio 3: 5:7. After a year, C invests another Tk.337600 while A withdraws Tk.45600. The ratio of investments then changes to 24:59:67. How much does A invest initially?

A.    Tk. 140600

B.     Tk.141600

C.     Tk.131600

D.    Tk.140500

Solution:

Let,

investment ratio A, B & C = 3x, 5x, 7x

ATQ,

3x-45600 : 5x = 24 : 59

Or, (3x – 45600)/5x = 24/59

Or, 177x – 59×45600 = 120x

Or, 57x = 59×45600

Or, x = 47200

.:.A’s investment = 3x = 3 × 47200 = 141600

111. A rectangular fish tank 25m by 9m has water in it to a level of 2m. This water is carefully poured into a cylindrical container with a diameter of 10m. How high will the water reach in the cylindrical container?

A.    18/π

B.     18

C.     7/18

D.    9/27

Solution:

Given,

Diameter 10 m

ATQ,

πr2h = 25 × 9 × 2

Or, π52h = 25 × 9 × 2

Or, h = (25 × 9 × 2) / 25 π

Or h= 18/π

112. At a symposium, 20% of the professors are psychologists, 60% are biologists and the remaining 12 professors are economists. If 20 of the professors wear glasses, what percent of the professors do not wear glass?

A.    20%

B.     33,%

C.     50%

D.    66%

Solution:

Let,

Total professors = x

ATQ,

x = 20% of x + 60% of x + 12

Or, x = x/5 + 3x/5 + 12

Or, x – x/5 – 3x/5 = 12

Or, x/5 = 12

Or, x = 60

Professors don’t wear glasses = x – 20 =  60 – 20 = 40

Required percentage = (40/60) × 100 = 66 2/3% = 66%

113. In a department, 3/5 of the workers are men and the rest are women. If 1/2 of the men and 3/7 of the women in the department are over 35, what fraction of all the workers in the department are over 35

A.    33/70

B.     66/70

C.     33/140

D.    35/140

Solution:

Men = 3/5

Women = 1 – 3/5 = 2/5

Workers over 35 are = ½ of 3/5 + 3/7 of 2/5 = 3/10 + 6/35 = 33/70

114. The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for months, find for how much time did Q invest the money?

A.    7 months

B.     10 months

C.     9 months

D.    11 months

Solution:

Let,

Q invested for x months

ATQ,

7×y : 5×x = 7:10

Or, 7y/5x = 7/10

Or, x= (10/7) × 7y × 1/5 = 2y

এখন y এর মান বসিয়ে দিলেই হবে।

115. A clock strikes once at1 o’clock twice at 2 o’clock, thrice at 3 o’clock and so on. How many times will it strike in 24 hours?

A.    78

B.     136

C.     156

D.    196

Solution:

(1+2+3+4………..+12) x 2 (১২ ঘন্টা পর্যন্ত ১ বার নেয়ার পর একই হিসেব দু বার না করে ২ দিয়ে গুণ)

= 12(l2 + 1)/2 = 156

116. The perimeter of a rectangle is 26 cm. The rectangle is converted to a square by tripling the width and taking a quarter of the length, What is the perimeter of the resulting square?

A.    9 cm

B.     12 cm

C.     20 cm

D.    26 cm

Solution:

Or, 2(L + B) = 26

Or, L + B = 13

Or, B = 13 – L

New L of square = 3L & B = (13-L) × ¼

ATQ,

3L = (13-L) × ¼

Or, 12L = 13 – L

Or, L = 1

So, length of the square = 3×1 = 3

So, perimeter of the square = 4×3 =12

117. In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then find the percentage of students who passed in both the subject.

A.    22%

B.     32%

C.     44%

D.    54%

Solution:

n(MUE) = n(M) + n(E) –n(M∩E) + passed in both

Or, 100% = 34% + 42% – 20% + passed in both

Or, passed in both = 44%

118. 125 gallons of a mixture contains 20% water. What amount of additional water should be added such that water content is raised to 25%?

A.    15/2 gallons

B.     17/2 gallons

C.     19/2 gallons

D.    25/3 gallons

Solution:

Water in the mixture = 20% of 125 = 25 gallons

So, other = 125-25 = 100

let, water be added = x

ATQ,

25+x = 25% of (125+x)

Or, 25 + x = (125+x)/4

Or, 100+4x =125+x

Or, 3x = 25

Or, x = 25/3.

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Updated: October 28, 2020 — 8:19 pm

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