BANK & INSURANCE (TIME AND WORK & PIPE AND CISTERN) PART 1

Total Questions: 60

41. A and B together can complete the work in 30 days. If B alone complete 20% of the work in 16 days. In how many days A alone complete 75% of the work?

Correct Answer: (b) 36 days  
Solution:A + B = 1/30
B = 5/1 × 16 = 80 days
A = 1/30 - 1/80
A = (8 - 3)/240 = 5/240
A = 1/48
A complete the 75% of the work in = 48 × 3/4 = 36 days

42. 2 men can complete a piece of work in 14 days. 2 women can complete the same piece of work in 24 days. In how many days will 7 men and 10 women together complete the same piece of work?

Correct Answer: (d) 2 2/11 days  
Solution:

Total work = men × days
2m × 14 = 2w × 24
7m = 12w
7m + 10w = 12w + 10w = 22w

Women days
2 24
22 ?

(2 × 24) = (22 × x)
x = 24/11 = 2 2/11 days

43. A can do the piece of work in 15 days. A and B together can complete the work in 12 days and A, B and C together can complete the work in 8 days. If they are gets the total wages is 1800, then what is the wage of B?

Correct Answer: (c) Rs.240
Solution:A = 1/15
B = 1/12 - 1/15 = 1/60
C = 1/8 - 1/12
C = 1/24
Ratio of work done by A, B and C = 1/15 : 1/60 : 1/24
= 8 : 2 : 5
B’s wages = 2/15 × 1800 = Rs.240

44. Arul, Banu and Chinu alone can complete the work in 20 days, 30 days and 12 days respectively. In how many days Arul, Banu and Chinu together can complete half of the work?

Correct Answer: (c) 3 days
Solution:Arul + Banu + Chinu together can complete the whole work = 1/20 + 1/30 + 1/12
= (3 + 2 + 5)/60
= 1/6
Half of the work completed in 3 days

45. 8 girls and 12 boys can complete a work in 4 days. If one boy alone completes the work in 60 days, then in how many days a girl will be able to finish the same work alone?

Correct Answer: (c) 160
Solution:Work done by 1 boy in 1 day = 1/60
Work done by 12 boys in 1 day = 12/60 = 1/5
Work done by 12 boys in 4 days = 4/5
In 4 days they will complete 4/5 of work, so 8 girls will finish 1/5 of work in 4 days.
So 1 girl will finish 1/40 of work in 4 days
Therefore, a girl alone will finish the work in 160 days

46. A, B and C can complete the work in 20 days, 15 days and 30 days respectively. They work together, in how many days they complete the 75% of the work?

Correct Answer: (b) 5 days  
Solution:The work done by A, B, C in one day,
A + B + C = (1/20 + 1/15 + 1/30)
= (3 + 4 + 2)/60 = 9/60 = 20/3 days
75% of the work will be completed in = 75/100 × 20/3 = 5 days

47. A is 20% less efficiency than B and B is 50% more efficiency than C. If C alone completed half of the work in 12 days, in how many days A, B and C together can complete the work?

Correct Answer: (a) 6 18/37 days  
Solution:C complete the whole work = 1/24
B alone complete the work = 24 × 100/150 = 16 days
A alone complete the work = 16 × 100/80 = 20 days
A + B + C = 1/24 + 1/16 + 1/20
= (10 + 15 + 12)/240
= 37/240 = 240/37 days = 6 18/37 days

48. A completes one-third of the work in 20 days and B completes half of the work in 15 days. In how many days A and B together can complete the work?

Correct Answer: (d) 20 days  
Solution:A completes the full work in = 3/1 × 20 = 60 days
B completes the full work in = 2 × 15 = 30 days
A + B = 1/60 + 1/30 = 3/60 = 1/20
A and B can complete the work in 20 days.

49. A and B can complete the work in 24 days and 16 days respectively. They started the work together and after 6 days B left the work. In how many days A alone complete the remaining work?

Correct Answer: (d) 9 days  
Solution:A = 1/24, B = 1/16
LCM of (16, 24) = 48
A complete the work in one day = 2 units
B complete the work in one day = 3 units
They work together in 6 days = 6 × (2 + 3) = 30 units of work completed
Remaining work = 48 - 30 = 18 units
A alone complete the remaining = 18/2 = 9 days

50. 6 men and 9 women can finish the work in 8 days and 8 men and 20 women can finish the same work in 4 days. In how many days a woman can finish the work?

Correct Answer: (c) 96 days
Solution:

(6m + 9w) × 8 = (8m + 20w) × 4
12m + 18w = 8m + 20w
4m = 2w
2m = w
6m = 3w
(3w + 9w) = 1/8
12w = 1/8
w = 1/96