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

Total Questions: 60

11. Worker A takes 6 hours to do a job. Worker B takes 8 hours to do the same job. How long should it take both A and B working together to complete the same job?

Correct Answer: (a) 3 3/7 hours  
Solution:As 1 hour work = 1/6; B’s 1 hour work = 1/8
(A + B)’s 1 hour’s work = (1/6 + 1/8)
= [(4+3)/24]
= 7/24
Both A and B working together completes a work in 24/7 hrs.
Therefore, both A and B will finish the work in 24/7 hours i.e., 3 3/7 hours

12. Shirisha can finish a certain job in 14 days, Madhu is 40% more efficient than shirisha. How many days does Madhu alone takes to finish the same job?

Correct Answer: (a) 10 days  
Solution:Given, Shirisha can finish a certain job in 14 days.
Madhu is 40% more efficient than Shirisha.
Madhu can finish a certain job = 14 × 100/140
= 10 days.
Therefore, Madhu alone takes 10 days to finish the job.

13. Raghu is twice as good as workman as Ram. Raghu and Ram together complete a piece of work in 16 days. In how many days will Ram alone do the same piece of work?

Correct Answer: (b) 48 days  
Solution:Raghu is twice as good a work man as ram.
Let, time taken by Raghu = x days
Time taken by Ram = 2x days
Since, raghu and ram together complete the work in 16 days.
Therefore, 1/x + 1/2x = 1/16
⇒ 2+1/2x = 1/16
⇒ 2x = 16×3
⇒ x = 16×3/2
⇒ x = 24
Thus, Time taken by ram = 2x = 2×24 = 48 days

14. Suresh and Ramesh together can complete a piece of work in 18 days. Ramesh alone can complete the same work in 27 days. In how many days can Suresh alone complete the same work?

Correct Answer: (a) 54 days  
Solution:Suresh and Ramesh together can complete a piece of work in 18 days.
Suresh and Ramesh together one day work = 1/18
Ramesh alone can complete the same work in 27 days.
Ramesh’s one day work = 1/27
Suresh’s 1 day’s work = 1/18 - 1/27 = 3-2/54 = 1/54
Suresh alone can complete a piece of work in 54 days.

15. A, B and C individually can finish the work in 6, 8 and 12 hours respectively. They started the work together and after completing the work got Rs 9000. What will be the share of A, B and C respectively?

Correct Answer: (e) None of these
Solution:Ratio of amount of work done by A, B and C respectively = (1/6):(1/8):(1/12) = 4:3:2
Therefore money obtained A = Rs (9000 × (4/9)) = Rs 4000
Money obtained B = Rs (9000 × (3/9)) = Rs 3000
Money obtained C = Rs (9000 × (2/9)) = Rs 2000

16. Three friends Ratish, Satish and Nitesh can do a work in 20, 24 and 32 days respectively. Ratish is assisted by Satish one day and by Nitesh the next day, alternatively. In how many days will the work be finished?

Correct Answer: (b) 11 7/13 days  
Solution:Ratish+Satish can do in 1 day = 1/20 + 1/24 = 11/120
Ratish+Nitesh can do in 1 day = 1/20 + 1/32 = 13/160
So in 2 days total work done = 11/120 + 13/160 = 83/480
Work done in first 10 days = 83×5/480 = 415/480
Remaining work = 1 - 415/480 = 65/480
Ratish + Satish in 1 day can do = 11/120 = 44/480
Remaining work = 65/480 - 44/480 = 21/480
Ratish+Nitesh can do 21/480 part work in (160/13) × (21/480) = 7/13 days
Total days required = 11 7/13 days.

17. Pallabi and Uia does a work in 10 and 15 days respectively. Pallabi and Uia together does the work for 4 days. Then Swati comes and performs the work for some days. Remaining work was completed by Uia in 2 days. How much part of the work was completed by Swati?

Correct Answer: (b) 0.2  
Solution:Pallabi and Uia together in 1 day does 1/10 + 1/15 = 1/6 part of the work.
Pallabi and Uia together completed 4/6 or 2/3 part of the work.
At last Uia does the work for 2 days, Uia does 2/15 part of the work.
Amount of work done by Swati = 1 - (2/15 + 2/3)
= 1/5 part of the work = 0.2 part of the work.

18. A and B can finish a work in 12 days, B and C together in 18 days. A and B start the work and A left after 4 days, C joins B on the 5th day and B left after the 6th day. C finished the work on 21st day, then in how many days can A himself finish the work?

Correct Answer: (d) 15 3/7 days  
Solution:A and B worked together for 4 days, B and C together worked for 2 days and C worked alone for 15 days.
So total work done by A and B in 4 days = 4×(1/12) = 1/3
So total work done by B and C in 2 days = 2×(1/18) = 1/9
So the total work done by C in 15 days = 1 - 1/3 - 1/9 = 5/9
So work done by C in 1 day = (5/9)/15 = 5/135 = 1/27
Means C can do the whole work in 27 days.
It is given that B and C together can do in 18 days.
Hence work done by B in one day = 1/18 - 1/27 = 1/54
Means B can complete in 54 days.
Similarly A and B do the work in 12 days.
So work done by A in one day = 1/12 - 1/54 = 7/108
Means A can complete the work in 108/7 = 15 3/7 days

19. 12 men and 16 boys can build a house in 40 days by working 8 hours per day. one man can complete the work in same time as that taken by two boys. 21 men started building another house which is twice as large as the previous house, working 9 hours a day. How many boys will be needed to build the given house if work has to be completed in approx. 50 days?

Correct Answer: (d) 15  
Solution:2 boys = 1 man
Hence; 12 men and 16 boys = 12 + 8 = 20 men
So total man hours to build the house = 20 × 8 × 40 = 6400 man hours.
The second house is twice as large so it will require 12800 man hours.
Let the number of boys required = 2n, hence total number of men = 21 + n
(21 + n) × 9 × 50 = 12800
⇒ 21 + n = 28.44 ≈ 28.5
⇒ n = 7.5
Hence total number of boys = 2n = 15

20. X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs. 720. With the help of Z they finished it in 5 days. How much is paid to Z?

Correct Answer: (b) Rs 120  
Solution:In one day X can finish 1/15th of the work.
In one day Y can finish 1/10th of the work.
Let us say that in one day Z can finish 1/Zth of the work.
When all the three work together in one day they can finish 1/15 + 1/10 + 1/Z = 1/5th of the work.
Therefore, 1/Z = 1/30.
Ratio of their efficiencies = 1/15 : 1/10 : 1/30 = 2 : 3 : 1
Therefore Z receives 1/6th of the total money.
According to their efficiencies money is divided as 240 : 360 : 120.
Hence, the share of Z = Rs. 120