## Combined Eight Bank Senior Officer-2018

SECTION-C: GENERAL MATHEMATICS

Questions (41-60): Read the following questions carefully and choose the right answer.

41. There are 3 green, 4 orange and 5 white color bulbs in a bag. If a bulb is picked at random, what is the probability of having either a green or a white bulb?

A. 3/4
B. 2/3
C. 4/3
D. 2/9

Option:  B

2/3

Exp: Total bulbs = 3+4+5 = 12

green + white bulbs = 3+5 = 8

So, probability of having green

or white bulbs = 8/12 = 2/3

42. A motor cycle covers 40 km with a speed of 20 km/hr. Find the speed of the motorcycle for the next 40 km journey so that the average speed of the whole journey will be 30 km/hr.

A. 70 km/hr
B. 52.5 km/hr
C. 60 km/hr
D. 60.5 km/hr

Option:  C

Exp: Average speed, 2xy/(x+y) = 30

Or, 2×20×y(20+y) = 30

Or, 40y = 600+30y

Or, 10y = 600

Or, y = 60

43. With a uniform speed, a car covers a distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 hours and 30 minutes. What is the distance covered?

A. 420 km
B. 480 km
C. 520 km
D. 640 km

Option:  B

Exp: Let, Distance = x km 7 hours and 30 minutes = 7.5 hr

ATQ, x/7.5 – x/8 = 4

Or, 10x/75 – x/8 = 4

Or, (80x – 75x)/600 = 4

Or, 5x/600 = 4

Or, x= (4×600)/5 = 480 km

44.The respective ratio between the speed of a car, a train, and a bus is 5:9:4. The average speed of the car, bus and train is 72 km/hr together. What is the average speed of the car and the train together?

A. 82 km/h
B. 72 km/h
C. 67 km/h
D. 84 km/h

Option:  D

Exp: Let the speed of car, train and bus = 5x, 9x , 4x km/hr

ΑΤQ, (5x+9x+4x)/3=72

Or, 18x = 216

Or, x=216/18

Or, x= 12

Average speed of car and train = (5x+9x)/2=7x=7×12=84 km/hr

45. A, B and C are partners of a company. During a particular year A received one-third of the profit. B received one-fourth of the profit and C received the remaining tk.5000. How much did A receive?

A. Tk. 5000
B. Tk 4000
C. Tk 3000
D. Tk. 1000

Option:  B

Exp: Total Profit = x So, A received = x/3 B received = x/4

ATQ,

x – x/3 – x/4 = 5000

Or, (12x – 4x – 3x)/12 = 5000

Or, 5x/12 = 5000

Or, x = 12000

A received = 12000/3 = 4000 Tk.

46. The average age of a group of 15 employees is 24 years. If 5 more employees join the group, the average age increases by 2 years. Find the average age of the new employees.

A. 35
B. 30
C. 24
D. 32

Option:  D

Exp: Total age of 15 employees = 15×24 = 360

After 5 more employees joining the group, the average age increases by 2 years.

That means, total age =(20×26) = 520

Total age of 5 employees =(520 – 360) = 160 So,

average = 160/5 = 32

47. By selling 32 guavas for tk. 30 at the rate of Tk. 1.066 per guava a man loss 25%. How many guavas should be sold for Tk. 18 to gain 20% of profit in the transaction?

A. 24
B. 12
C. 18
D. 36

Option:  B

Exp: At 25% loss, cost price of 32 guavas= 30×100/75 = 40 tk at 20% profit,

selling price of 32 guavas=40×120/100=48 tk

So, 48 tk is the selling price of 32 guava

1 ————————– =32/48

18 ———————— =(32×18)/48=12 guavas

48. A sold a watch to B at a gain of 20% and B sold it to C at a loss of 10%. If C bought the watch for Tk.216, at what price did A purchase it?

A. Tk. 200
B. TK. 216
C. TK. 250
D. Tk. 176

Option:  A

Exp: At 10% loss,

Cost price to B = (216×100)/90 = 240 tk

At 20% gain, Cost price to A = (240×100)/120 = 200 tk

49. A square is inscribed in a circle of diameter 2a and another square is circumscribing circle. The difference between the areas of outer and inner squares is

A. a2
B. 2a2
C. 3a2
D. 4a2

Option: B

Exp: ATQ, Diagonal of inner square = 2a

So, one hand of the inner square = 2a/√2 = √2a

So, area of the inner square = (√2a)2 = 2a2

Again, One hand of the outer square = 2a

So, area of the outer square = (2a)2 = 4a2

So, difference = 4a2 – 2a2 = 2a2

50. The average of the three numbers x, y and z is 45. X is greater than the average of y and 2 by 9. The average of y and z by 9. The average of y and z is greater than y by 2. Then the difference of x and z is

A. 3
B. 5
C. 7
D. 11

Option:  C

Exp: Sum of x,y and z = 45×3

So, ∴x+y+z =135—– (i)

Again, X = (y+z)/2 +9

Or, 2x = y+z+18 ——-(2)

Again, (y+z)/2 = y+2

Or, 2y+4 = y+z

Or, y = z-4 From (2),

2x = z-4+z+18

Or, 2x – 2z = 14

Or, x-z = 7

51. A boat travel with a speed of 10 km/hr in still water. If the speed of the stream is 3 km/hr then find time taken by boat to travel 52 km downstream.

A. 2 hrs
B. 4 hrs
C. 6 hrs
D. 9 hrs

Option:  B

Exp: Speed in downstream = 10+3 = 13km/hr

So, time taken to travel 52km

downstream =52/13= 4hrs

52. Rahima can row 16 km/hr in still water. It takes her thrice as long to row up as to row down the river. Find the difference between her speed in still water and that of the stream.

A. 8 km/hr
B. 16 km/hr
C. 24 km/hr
D. 12 km/hr

Option:  A

Exp: Let, the speed of Stream = x,

so, downstream speed = 16+x

and upstream speed = 16-x

ATQ, 16+x = 3(16-x)

Or, 16+x = 48 -3x

Or, 4x = 32 Or, x =8

So speed of stream = 8

and difference of speed of still water & stream = 16 – 8 = 8km/hr

53. A train leaves a station A at 7 am and reaches another station B at 11:00 am. Another train leaves B at 8 am and reaches A at 11:30 am. The two ruins cross one another at

A. 8:36 am
B. 8:56 am
C. 9.00 am
D. 9:24 am

Option: D

Exp: Let, distance between A and B = x mile

So, Speed of first train = x/4 km/hr Speed of second train = x/3.5 km/hr

Let after y hrs, two train will meet.

So, x/4 ×(y+1) + x×y/3.5 = x

Or, (y+1)/4 = y/3.5 = 1

Or, (3.5y + 3.5 + 4y)/14 = 1

Or, 7.5y + 3.5 = 14

Or, 7.5y = 10.5

Or, y = 7/5 = 1 hr 24 min

So, the train will meet = 8+1hr 24 min = 9:24 Am

54. A train 150 m long crosses a milestone in 15 seconds and crosses another train of the same length travelling in the opposite direction in 12 seconds. The speed of the second train in km/hr is

A. 52 km/hr
B. 56 km/hr
C. 54 km/hr
D. 58 km/hr

Option:  C

Exp: Speed of 1st train=150/15=10 m/s

Relative speed of two train = (150+150)/12 = 25 m/s

So speed of 2nd train = 25-10=15 m/s = 15×(18/5)=54 kmh

55. There are 2 numbers in the ratio of 4:5. If 4 is subtracted from both numbers the ratio becomes 3:4. What will be the ratio if 4 is added in the both numbers?

A. 1:2
B. 2:3
C. 5:6
D. 1:4

Option:  C

Exp: Let the numbers are 4x and 5x

ATQ,

(4x-4)/(5x-4) = ¾

Or, 16x – 16 = 15x – 12

Or, 16x – 15x = 4

Or, x = 4

So, Required ratio = (16+4) : (20+4) = 20:24 = 5:6

56. The income of A is 20% higher than that of B. The income of B is 25% less than C. What percent less is A’s income from C’s income?

A. 7%
B. 8%
C. 9%
D. 10%

Option:  D

Exp: Let, B’s income = 100

So, A’s income = 120

again, if income of C = 100

then B’s = 100-25 = 75

So, when B’s income 75 then C = 100

When, B’s income 1 then C = 100/75

When, B’s income 100 then C = (100×100)/75 = 133.33

A is less than C = C-A = 133.33-120 = 13.33 less % = (13.33×100)/133.33 = 10%

57. The ratio of two numbers is 7: 4. If 8 is added to both the numbers ratio becomes 13:8. What is the smaller number?

A. 40
B. 56
C. 38
D. 52

Option: A

Exp: Let, the number be 7x and 4x

ATQ,

(7x+8)/(4x+8) = 13/8

Or, 56x + 64 = 52x + 104

Or, 4x = 40

Or, x = 10

So, smaller number = 4x = 4×10 = 40

58. A and B can do a work in 12 days. B can do the same work in 18 days. In how many days A can complete the 2/3 of the same work?

A. 36 days
B. 24 days
C. 16 days
D. 27 days

Option:  B

Exp:

A alone can do (1/12 – 1/18) = 1/36 part of the work

So, A alone can do 1/36 part of the work in 1 day

So, A alone can do 2/3 of the work in 36 × 2/3 day = 24 days

59. A is twice as good as B and together they finish a piece of work in 16 days. The number of days taken by A alone to finish the work is

A. 20 days
B. 21 days
C. 22 days
D. 24 days

Option:  D

Exp: Let, A needs = x days

so, B needs 2x days

ATQ,

1/x + 1/2x = 1/16

Or, 3/2x = 1/16

Or, 2x = 48

Or, x = 24

60. A box contains 5 pink, 3 green and 2 yellow balls. Three balls are picked up randomly. What is the probability that none of the ball drawn is green?

A. 3/16
B. 7/24
C. 5/18
D. 4/24

Option:  B

Exp: Total number of balls = 5+3+2 = 10

total number of non green balls = 5+2 = (pink+yellow)

Total number of ways of selecting 3 balls from 10 balls = 10C3 = 120

Number of ways of selecting 3 non green balls from 7 non green balls = 7C3 = 35

So, required probability = 35/120 = 7/24