Question

A can do a piece of work in 20 days, B in 30 days and C in 40 days. They start
working together. A works for 2 days and leaves and B leaves 4 days before the
work finishes. How long does the work last​

Answer 1

A's one day work =1/20

Bs one day work= 1/30

C's one day work= 1/40

(A+B+C)'s one day = (1/20)+(1/30)+(1/40) = 13/120

For 2 days A B and C worked together , so (A+B+C)'s 2 days work = 2x(13/120) = 13/60

Remaining work = 1–13/60 = 47/60

(B+C) together will work on it for 2 days after A left , so we'll find (b+c)'s 2 days work = 2[(1/30)+(1/40)] =7/60

Now find the.remaining work = (47/60) - (7/60) = 40/60 or 2/3

This 2/3 work will be done by C alone so we'll divide this by C's one day work

(2/3)÷(1/40) = 80/3 = 2.67 days

Total time taken = 4 + 2.67 = 6.67 days ANS

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