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Mahesh Sandeboina

· started a discussion

· 1 Months ago

can any one explain it properly (Question: 269901.0 )

please am not able to understand the solution given

Question:

To do a certain work, B would take time  52    times as long as A and C takes together and C takes,  72    times as long as A and B take together. The three men together can complete the work in 20 days. The time taken by C to complete the work separately is–

Options:
A)

60 days

B)

90 days

C)

45 days

D)

120 days

Solution:

Ans: (b)

  

Harendra upadhyay

· commented

· 1 Months ago

if B takes 5/2 as much time as A&C together then the ratios of efficiencies of B:A+C=2:5 and similliarly C:A+B=2:7
B:(A+C):(A+B+C)=2:5:7............(1)

C:A+B:(A+B+C)=2:7:9..............(2)
making ratio numbers for (A+B+C) same in both the equations, we multiply equation (1) by 9 while equation (2) by 7 then we get following numbers:
B:(A+C):(A+B+C)=18:45:63

C:A+B:(A+B+C)=14:49:63 now by seeing this we we can easily determine that efficiencies of A= 31, B=18 & C=14
and A+B+C complete the whole work in 20 days then total work will be 20 X (31+18+14) = 1260 and now we are asked to find out the time taken by the C then it can be calculated by dividing 1260 by efficiency of C(i.e.14) and answer will be 90 days. Hope it'll clear your doubt to some extent.......
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