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**A can do a piece of work in 40 days. He works at it for 8 days and then B finishes the remaining work in 16 days. How long will they take to complete the work if they do it together?**

Answer:

Given:

A can do a piece of work in = 40 days

A’s, 1 day work = 1/40

A’s, 8 day work = 8/40 = 1/5

Remaining work = 1 – 1/5

= (5-1)/5

= 4/5

B can do 4/5 piece of work in = 16 days

B’s, 1 day work = (4/5)/16

= 4/(5×16)

= 1/20

Now, (A+B)’s 1 day work = 1/40 + 1/20

= (1+2)/40

= 3/40

∴ Both (A+B) can do a piece of work in = 1/(3/40) days

= 40/3 days

= 13 1/3 days

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