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

Total Questions: 60

41. A, B and C can do a piece of work in 14, 28 and 32 days respectively. They all begin to working together. A work continuously till it is finished, B leaves the work 3 days before its completion and C leaves the work 2 days before its completion. In what time is the work finished?

Correct Answer: (b) 8 14/31 days  
Solution:

Let the work finished in x days

A’s one day work = 1/14
B’s one day work = 1/28
C’s one day work = 1/32

x/14 + (x-3)/28 + (x-2)/32 = 1

⇒ (16x + 8x - 24 + 7x - 14)/224 = 1
⇒ 31x = 224 + 38
⇒ x = 262/31
⇒ x = 8 14/31 days

42. A and B together can complete the job in 16 days, B and C together can complete the job in 20 days. First A did the job for 6 days, B did the job for 9 days and C completed the remaining job in 22 days. Find the number of days in which C alone can complete the job?

Correct Answer: (a) 40 days   
Solution:

LCM of 16 and 20 = 80 units

(A + B)’s one day work = 5 units
(B + C)’s one day work = 4 units

A’s 6 days work + B’s 9 days work + C’s 22 days work
= 80

(A + B)’s 6 days work + (B + C)’s 3 days work + C’s 19 days work = 80

(5×6) + (4×3) + C’s 19 days work = 80
C’s 19 days work = 80 - 30 - 12 = 38

C’s one day work = 38/19 = 2 units

C alone can complete the work in, (80/2) = 40 days

43. A and B together can complete 33 1/3 % of the work in 10 days, C and D together can complete 85% of the work in 17 days and A, B and C together can complete half of the work in 7.5 days. A and D together can complete 66 2/3 % of the work in 16 days. In how many days B alone complete 40% of the work?

Correct Answer: (d) 48 days  
Solution:

A + B = 300/100 × 10 = 30 days
C + D = 100/85 × 17 = 20 days

A + B + C = 2/1 × 7.5 = 15 days
C = 1/15 - 1/30 = 1/30
D = 1/20 - 1/30 = 1/60

A + D = 300/200 × 16 = 24 days
A = 1/24 - 1/60 = (5 - 2)/120 = 1/40

B = 1/30 - 1/40 = 1/120

B complete 40% of the work = 40/100 × 120 = 48 days

44. A can complete the 75% of the work in 9 days and A and B together can complete 60% of the work in 4.8 days. If A got Rs. 5000 for doing the whole work and then what is the difference between the amount received by A and B?

Correct Answer: (b) Rs.2500  
Solution:

A = 4/3 × 9 = 12 days
A + B = 100/60 × 4.8 = 8 days

B = 1/8 - 1/12 = 3 - 2/24 = 1/24

Ratio of the amount received by A and B = 1/12 : 1/24
= 2 : 1

Required difference = 1/2 × 5000 = 2500

45. A alone complete four – ninth of the work in 20 days, B alone complete half of the work in 15 days and C alone complete four – fifth of the work in 36 days. A and B started the work and after 5 days C joined with them, in how many days the work will be completed?

Correct Answer: (b) 14 2/7 days  
Solution:

A = 9/4 × 20 = 45
B = 2/1 × 15 = 30
C = 5/4 × 36 = 45

(x + 5/45) + (x + 5/30) + (x/45) = 1
2x + 10 + 3x + 15 + 2x = 90
7x = 65
x = 65/7 = 9 2/7

Total time = 5 + 9 2/7 = 14 2/7 days

46. A can complete 75% of the work in 15 days and B alone complete 60% of the work in 18 days. If A and B works alternatively starting from A and then B so on, in how many days half of the total work is completed?

Correct Answer: (e) None of these
Solution:

A = 100/75 × 15 = 20 days
B = 100/60 × 18 = 30 days

First 2 days complete the work = 1/20 + 1/30 = 5/60 = 1/12

After 6 times of 2 days = 6/12 = 1/2
After 6 × 2 = 12 days half of the work is completed

47. A and B together can complete 60% of the work in 8 16/25 days and B and C together can complete 80% of the work in 7 1/5 days. If B and C started the work and after 4 days they left the work, then A complete the remaining work in 13 1/3 days, in how many days A, B and C alone complete the work respectively?

Correct Answer: (e) 24, 36, 12
Solution:

A + B complete the whole work = 100/60 × 216/25
= 14 (2/5) days

B + C complete whole work = 100/80 × 36/5 = 9 days
B + C complete the work in 4 days = 4/9
Remaining work = 5/9

A alone complete the whole work = (40/3)/(5/9) = 24 days

B = 5/72 - 1/24 = 2/72 = 1/36
C = 1/9 - 1/36 = 3/36 = 1/12

48. 18 men can complete a work in (x – 6) days. 20 women can complete the same work in (x – 2) days. 10 men can complete the same work in (y + 2) days. 16 women can complete the same work in (y + 4) days. Find the value of x – y?

Correct Answer: (b) 40/11  
Solution:

18 men can complete the work in (x - 6) days
One man can complete the work in 18 × (x - 6) days
10 men can complete the same work in (y + 2) days
One man can complete the same work in 10 × (y + 2) days

Since, the work is same

18 × (x - 6) = 10 × (y + 2)
9 × (x - 6) = 5 × (y + 2)
9x - 54 = 5y + 10
9x - 5y = 64 ..........(i)

Also, 20 women can complete the work in (x - 2) days
1 woman can complete the work in 20 × (x - 2) days
16 women can complete the work in (y + 4) days
One woman can complete the work in 16 × (y + 4) days

Since, the work is same

20 × (x - 2) = 16 × (y + 4)
5 × (x - 2) = 4 × (y + 4)
5x - 10 = 4y + 16
5x - 4y = 26 ..........(ii)

Solving equation 1 and equation 2, we get
x = 126/11 and y = 86/11

Therefore,
x - y = (126/11) - (86/11) ⇒ x - y = 40/11

49. (x – 5) person can do a work in x days and (x + 10) person can do the same work in (x – 10) days. Then in how many days can (x + 5) person finish the work?

Correct Answer: (d) 12 days  
Solution:

(x - 5) person can do the work in = x days
(x - 5)x = (x + 10)(x - 10)
x² - 5x = x² - 100
5x = 100
x = 20

Person  days
15    20
25    ?

(15 × 20) = 25y
y = 300/25 = 12 days

50. A, B and C together can complete the work in 9 days. If ratio of efficiency of B to A is 3:2, C and D together can complete 75% of the work in 6 days the efficiency of C is x% of D, then find the value of x?

From the statement given in the above question which of the following can be determined.
(A) Value of x
(B) Time taken by A alone complete the work.
(C) Time taken by C and B together can complete work.
(D) If the efficiency of B and C is equal, then in how many days D alone complete the work

Correct Answer: (b) Only D  
Solution:

A + B + C = 1/9
C + D = 100/75 × 6 = 8

1/3y + 1/2y + 1/2y = 1/9
(2 + 3 + 3)/6y = 1/9
8/6y = 1/9
1/y = 1/12

C alone complete the work = 2 × 12 = 24 days
D = 1/8 - 1/24 = 2/24 = 1/12