BANK & INSURANCE (TIME AND WORK & PIPE AND CISTERN) PART 2

Total Questions: 60

51. Aliya, Bala and Sara together can complete the work in 20 days and Aliya alone completes 80% of the work in 36 days. If Bala alone completes 75% of the work in 45 days, in how many days Sara alone completes 80% of the work?

Correct Answer: (d) 72 days  
Solution:

A + B + S = 1/20
A = 100/80 × 36 = 45 days
B = 100/75 × 45 = 60 days

S = 1/20 - 1/45 - 1/60
= (9 - 4 - 3)/180 = 1/90

Sara alone completes 80% of the work = 80/100 × 90
= 72 days

52. Ratio of the efficiency of A and B is 3:2 and the ratio of the efficiency of A and C is 3:1. If B and C together can complete the work in 12 days, in how many days A and B together can complete the work?

Correct Answer: (d) 7 1/5 days  
Solution:

Efficiency of A and B = 3 : 2
Efficiency of A and C = 3 : 1

Efficiency of A, B and C = 3 : 2 : 1
Time ratio of A, B and C = 2 : 3 : 6

1/3x + 1/6x = 1/12
3/6x = 1/12
x = 6

A alone completes the work = 2 × 6 = 12 days
B alone complete the work = 3 × 6 = 18 days

A + B = 1/12 + 1/18
= 5/36

Required time = 7 1/5 days

53. The efficiency of B is 12.5% less than the efficiency of A. B alone can complete half of the work in 12 days. If A and B together started the work and after x days A left the work and B alone completed the remaining work in 9 days, then find the value of x.

Correct Answer: (a) 7  
Solution:

B alone can complete the whole work in = 12 × 2/1 = 24 days
A alone can complete the whole work in = 87.5/100 × 24 = 21 days

x/21 + (x + 9)/24 = 1
8x + 7x + 63 = 168
15x = 105
x = 7

54. A and B together can complete 45% of the work in 10 days and C alone can complete 80% of the work in 24 days. If C and B together can complete 16% of the work in 3 days, in how many days A and C together can complete 70% of the work?

Correct Answer: (a) 12 days  
Solution:C alone complete whole work = 100/80 × 24 = 30 days

A + B complete the whole work = 10 × 100/45 = 200/9

C and B together complete the whole work = 3 × 100/16 = 150/8

B alone complete the work = 8/150 - 1/30 = 1/50
A alone complete the work = 9/200 - 1/50 = 1/40

A and C together can complete whole work = 1/40 + 1/30 = 7/120

Required answer = 120/7 × 70/100 = 12 days

55. A can complete 80% of the work in 12 days and B can complete 60% of the work in 7.2 days. If A and B started the work and after 3 days they left the work and C alone completed the remaining work in 33 days, then in how many days C alone completes the whole work?

Correct Answer: (b) 60 days  
Solution:

A = 100/80 × 12 = 15 days
B = 100/60 × 7.2 = 12 days

A and B together complete (3/15 + 3/12) part of work in 3 days

Remaining work = 1 - 9/20 = 11/20

C alone complete the whole work
= 33 × 20/11 = 60 days

56. A can complete the work in 36 days which is 12 days less than the time taken by B to complete the same work and the ratio of the efficiency of B and C is 5:4. In how many days A, B and C together can complete the work?

Correct Answer: (e) 15 15/47 days
Solution:

A = 36 days
B = 36 + 12 = 48 days
C = 5/4 × 48 = 60 days

A + B + C = 1/36 + 1/48 + 1/60
= (20 + 15 + 12)/720
= 47/720

Required time = 15 15/47 days

57. A alone completes the work in 18 days and B alone completes the work in 20 days. If B started the work and after 10 days left the work, then A and C together can complete the remaining work in 6 days, in how many days C alone completes the whole work?

Correct Answer: (c) 36 days
Solution:

A = 1/18
B = 1/20

B completes 10/20 of work in 10 days

Remaining work = 1 - 1/2 = 1/2

A and C together can complete the 1/2 of the work in 6 days

A and C together can complete whole work in 12 days

C = 1/12 - 1/18 = 1/36

58. 15 men can do a work in 8 days, while 12 women can do the same work in 16 days. In how many days 10 men and 8 women together can do the same work?

Correct Answer: (a) 8 days  
Solution:

15 men’s one day work = 1/8
Therefore 1 man’s one day work = 1/(8×15)

12 women’s one day work = 1/16
Therefore 1 woman’s one day work = 1/(12×16)

Required time = 10 men + 8 women = [10/(8×15)] + [8/(12×16)] = (1/12) + (1/24)

= (2+1)/24 = 3/24 = 1/8
10 men and 8 women together can complete a work in 8 days

59. The efficiency of C is 50% more than that of A and 20% more than that of B. Time taken by A and B together to complete the work is 12 days. Find the number of days taken by all of them together to complete the same work?

Correct Answer: (a) 7 1/5 days  
Solution:

Efficiency ratio of C to A = 150 : 100 = 3 : 2
Efficiency ratio of C to B = 120 : 100 = 6 : 5
Efficiency ratio of A : B : C = 4 : 5 : 6

Total work = (A + B) × 12 = (4 + 5) × 12 = 108 unit
Total number of days taken = 108/(4+5+6)
= 108/15 = 7 (1/5) days

60. If 18 men and 24 women do a piece of work in 9 days and 9 men and 27 women do the same piece of work in 12 days, how long will 6 men and 10 women take to complete the same work?

Correct Answer: (a) 24 6/11 days  
Solution:

(18m + 24w) × 9 = (9m + 27w) × 12
54m + 72w = 36m + 108w
36w = 18m
m = 2w

(18 + 12)m = 1/9
m = 1/270

6m + 10w = 6m + 5m
Required time = 11/270
= 24 6/11 days