Question

A and b together can do a piece of work in 30 days. A having worked for 16 days, b finishes the remaining work alone in 44 days. In how many days shall b finish the whole work alone?Lcm method

Answer 1

Given that A and b together can do a piece of work in 30 days.

This implies in one day A and b together can do 1/30 of full work.

A works for 16 days and B works for 44 days alone.

Let A take x days and B take y days to complete the work alone.

Then one day contribution of A is 1/x and B is 1/y

16/x+44/y = 1 (since they complete full work by doing 16 and 44 days)

Also 1/x +1/y = 1/30 (since both together can do in 30 days)

Multiply II equation by 30 and subtract from first.

28/y = 14/30

Or y = 60 days

B takes 60 days to complete the project alone.