Question

A completes a work in 120 days, B completes the same work in 150 days. Both work for 20
days and then B leaves the work and A continues the work. After 12 days C joins. A and C
completed work in 48 days, then calculate the number of days in which C completes the work.
​

Answer 1

Answer:

A→ 120

B→ 150

Total work = LCM (120,150) = 600

So,

A’s one day work will be 600/120 = 5

B’s one day work will be 600/150 = 4

Now, A+B work together for 20 days:

(A+B)’s total efficiency will be 5+4 = 9

Since they work together for 20 days, 9*20 = 180 which is the total work done.

Remaining work = 600–180 = 420.

B leaves, A alone continues the work for another 12 days:

A’s efficiency is 5 and he works for 12 days. So, 5*12 = 60 which is the work completed by A in 12 days.

Now, the remaining work will be 420 -60 = 360.

Then, A+C work for 48 days:

So, Total work / (efficiency of A+C) is 360/ 48 = 7.5 which is (A+C)’s one day work.

As we already know, A’s efficiency is 5,

C’s efficiency will be 7.5 - 5 = 2.5

Hence,

C alone complete the work in 600/ 2.5 = 240 days