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

Total Questions: 60

51. A and B together can complete the work in 13 days and A alone complete the work in 39 days. If A and B together can start the work, after 6 days A left the work, in how many days can B complete the remaining work?

Correct Answer: (e) None of these
Solution:A + B = 1/13
A = 1/39
B = 1/13 - 1/39 = 2/39
6/39 + ((6 + x)/2)/39 = 1
(12 + 2x)/39 = 11/13
21 = 2x
x = 10.5 days

52. A alone complete the work in x days and A and B together can complete the work in (x - 4) days. Efficiency of A is double of the efficiency of B. Find the value of x.

Correct Answer: (a) 12  
Solution:

A + B = x - 4 days
A = x days
Time ratio of A and B = 1 : 2
B alone complete the work = 2 × x = 2x
1/x + 1/2x = 1/(x - 4)
3/2x = 1/(x - 4)
2x = 3x - 12
x = 12

53. Arun works twice as fast as Bala. If Bala can complete a work in 24 days independently, then in how many days Arun and Bala together can finish the work?

Correct Answer: (c) 8
Solution:Rate ratio = 2 : 1
Time taken = 1 : 2
Bala’s 1 day’s work = 1/24
Arun’s 1 day’s work = 1/12
(Arun + Bala)’s 1 day’s work = 1/24 + 1/12 = 1/8
Arun and Bala together can finish the work in 8 days

54. A alone completes the work in 16 days and the efficiency of A is 25% less than the efficiency of B. If A, B and C together can complete the work in 6 days, in how many days C alone complete the work?

Correct Answer: (c) 48
Solution:

A alone completes the work = 16 days
Efficiency of A and B = 75 : 100
Time ratio of A and B = 4 : 3
B alone complete the work = 3/4 × 16 = 12 days

C alone complete the work 1/T = 1/6 - 1/12 - 1/16
= (8 - 4 - 3)/48 = 1/48
= T = 48 days

55. A, B and C together can complete the work in 16 days. If A, B and C started the work together, after 4 days A is left the work and then C and B together can complete the remaining work in 24 days. In how many days A alone complete the work?

Correct Answer: (a) 32 days  
Solution:A, B and C together can complete the work in 4 days
= 4/16 = 1/4
Remaining work = 1 - 1/4 = 3/4
C and B together can complete the whole work
= 4/3 × 24 = 32 days
A alone complete the work 1/T = 1/16 - 1/32 = 1/32
T = 32 days

56. A, B and C together can complete half of the work in 5(7/13) days. If B and C together can complete 60% of the work in 9.6 days, in how many days A alone complete the work?

Correct Answer: (d) 36 days
Solution:A + B + C together can complete the whole work = 144/13 days
B + C together can complete the whole work = 100/60 × 9.6 = 16 days
A alone complete the work 1/T = 13/144 - 1/16
= 4/144 = 1/36 ⇒ T = 36 days

57. A alone can finish a work in 12 hours while B finishes the same work in 8 hours. If both started work together and after 3 hours A left the work, then B alone finish the remaining work in how many hours?

Correct Answer: (a) 3 hours  
Solution:

LCM of 12 and 8 = 24 units (Total work)
Now, efficiency of A = 24/12 = 2 units/day
Efficiency of B = 24/8 = 3 units/day
So, both work together for 4 hours = 3 × (3+2) = 15 units
Remaining work = 24 - 15 = 9 units
Hence, 9 units of work will be done by B in 9/3 = 3 hours

58. The efficiency of A is 200% more than the efficiency of C and the efficiency of D is 25% less than the efficiency of C. If A and B together can complete the work in 14 days and C and D together can complete the work in 36 days, in how many days B alone complete the work?

Correct Answer: (a) 42 days  
Solution:

Efficiency of A and C = 300:100 = 3:1
Time ratio of A and C = 1:3

Efficiency of C and D = 100:75 = 4:3
Time ratio of C and D = 3:4
1/3x + 1/4x = 1/36
7/12x = 1/36
x = 21
C alone complete the work = 3 × 21 = 63 days
A alone complete the work = 1/3 × 63 = 21 days
B alone complete the work 1/T = 1/14 - 1/21 = 1/42
T = 42 days

59. A alone completes the work in 30 days and the efficiency of A is 300% more than the efficiency of B. If A, B and C together can complete the work in 16 days and they are get the total wages of Rs.27000, then what is the wages of C?

Correct Answer: (a) Rs.9000  
Solution:A = 1/30
Efficiency of A and B = 400:100 = 4:1
Time ratio of A and B = 1:4
B alone complete the work = 4 × 30 = 120 days
C alone complete the work = 1/16 - 1/30 - 1/120
= (30 - 16 - 4)/480 = 1/48
Ratio of work done by A, B and C
= 1/30 : 1/120 : 1/48
= 16 : 4 : 10 = 8 : 2 : 5
C’s wage = 5/15 × 27000 = Rs.9000

60. 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: (a) 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