Question

A can do a piece of work in 10 days B in 12 days and C in 15 days they all start the work together but a leaves the work after 2 days and B leaves 3 days before the work is completed how many days did the work last

Answer 1

Answer:

7 days

Step-by-step explanation:

Given A can do the work in 10 days ,B can do the work in 12 days and C can do the work in 15 days.

Then A's one day's work =  1/10

B's one day's work =1/12

C's one day's work =1/15

Then (A+B +C)'s one day's work =  1/10+1/12+1/15 = 450/1800 = 1/4

(A+B+C)'s  two days' work = 1/4*2 = 1/2

But B leaves 3 days before the work gets finished, so C does the remaining  work alone

C's 3  days' work = 1/15*3 = 1/5

Then work done in 2+3 days = 1/2+1/5 = 7/10

Work done by B+C together  = 1 − 7/10 = 3/10

(B + C)'s one day work = 1/12+1/15 = 3/​20

So number of days worked by B and C together=  3/10*20/3 = 2 days

Then total work done =2+3+2=7 days