Question

A alone can do a piece of work in 8days . A and B together can finish the
same work in 6 days , If B alone is doing the work, how long will it take?

Answer 1

Answer:

24

Step-by-step explanation:

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CBSE

Mathematics

Grade 8

Unitary Method

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A alone can do a piece of work in 8 days. A and B together can finish the same work in 6 days. If B alone is doing the work, how long will it take?

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Hint: The given problem is a work and time problem. We will use the unitary method to solve this problem. We are given the time consumed by A to finish a work and the time consumed by A and B together to finish the work. Using these given things we are asked to find the time consumed by B alone to finish the work. We will also introduce algebraic expressions to solve this problem.

Complete step-by-step answer:

A can do a piece of work in 8 days.

Let the work done by A in one day is 18 th of the work done.

A and B together can do the same work in 6 days.

So, the work done by A alone is 6×18 of the total work.

6×18=68

Now the rest work be done by B let it be x .

So, 68+x=1

⇒x=1−68=28

The work is for 6 days.

So, the actual work done by B for 1 day is 16×28=124

Since, B takes 1 a day to complete 124 part of the work.

This means B takes 24 days to finish the work alone.