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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
Answer: 5376
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
Answer: 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
Answer: 16
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
Answer: 143
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
Answer: Tk. 7500
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
Answer: 18 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
Answer: 23
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
Answer: 24
Solution:
Let, Additional match = x
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
Answer: A 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
Answer: 24
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
Answer: ½
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
Answer: 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
Answer: 10p+20q
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
Answer: 1.65 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
Answer: ½
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
Answer : 8/3
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%
Answer: 6%
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
Answer: 17m
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%
Answer: 20%
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
Answer: Tk. 850
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
Answer: 7
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
Answer: 4
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
Answer: 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
Answer: 5376
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
Answer: 12
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
Answer: Tk. 150
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
Answer: 1
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?
- 2
- 3
- 4
- 6
Answer: 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
Answer: 13 days
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
Answer : 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
Answer: 23
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
Answer: 7, -9
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
Answer: 18
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
Answer: 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
Answer. 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
Answer: 500 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
Answer: 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
Answer: 15
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
Answer: A 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
Answer: Tk. 169,440
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
Answer: 60
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%
Answer: 50%
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
Answer: less 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
Answer: 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)
Answer: 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
Answer: 12 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
Answer: 500km
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
Answer: 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
Answer: 63
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
Answer: 2000
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
Answer: 82%
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
Answer: 57
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
Answer: 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
Answer: 5
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
Answer: 36
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%
Answer: 125%
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
Answer: 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
Answer: 8 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
Answer: 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
Answer: 5km
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
Answer: 12 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
Answer: 9.60 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
Answer: -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
Answer: 20 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
Answer: 7/19
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
Answer: 3/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
Answer: 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
Answer: 18/7
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
Answer: 5/3
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
Answer: Tk. 121
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
Answer: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
Answer: 10 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
Answer: 1/5
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
Answer: Tk. 141600
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
Answer: 18/π
Solution:
Given,
Diameter 10 m
So radius = 10/2= 5m
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%
Answer: 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
Answer: 33/70
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
Answer: (Wrong question)
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
Answer: 156
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
Answer: 12 cm
Solution:
2(length + breadth) = perimeter
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%
Answer: 44%
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
Answer: 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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