A and B together can do a piece of work in 10 days if an alone will take 12 days to finish the work how long will B take to do the work?

Given:

A and B together can do a piece of work in 10 days.

A alone will take 12 days to finish the work in 12 days

To do:  To find how long will B take to finish the same work

Solution:
This implies,

Work is done by A and B together in 1 day=$\frac{1}{10}$

A alone takes 12 days to finish the work.

Work is done by A in a day = $\frac{1}{12}$

Let the number of days taken by B to finish the work be x.

Work done by B in a day = $\frac{1}{x}$

Therefore, $\frac{1}{10}=\frac{1}{12}+\frac{1}{x}$

$\frac{1}{10}=\frac{x\times1+12\times1}{12x}$

$\frac{1}{10}=\frac{x+12}{12x}$

$12x=10(x+12)$

$12x=10x+120$

$12x-10x=120$

$2x=120$

$x=60$

Therefore, B alone will take 60 days to finish the same work.

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Updated on: 10-Oct-2022

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