Question

A and B together can do a piece of work in 16 days and A alone can do it in 48 days.
How long will B take to complete the work?

Answer 1

Solution -

According to the question

A and B together can do the entire piece of work inn16 days.

Hence, in a day , A and B can together do 1/16 th of the work .

Now it is also mentioned that A can alone do it in 48 days.

Hence, in a single day , A can do 1/48th of the work.

Here we need to find how long B takes to do the work .

Let us assume that B does the work in x days.

Work done by B in one day > 1/x

So

1/x + 1/48 = 1/16

> 1/x = 1/16 - 1/48

> 1/x = 3/48 - 1/48

> 1/x = 2/48 = 1/24

> x = 24 days .

Thus , B takes 24 days to complete the work. This is the required answer .

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Answer 2

Given :-

A and B together can do a piece of work in 16 days and A alone can do it in 48 days.

To Find :-

How  long will B take to complete the work?

Solution :-

At first

Let work done by B in one day be 1/y

Now

$\sf \dfrac{1}y = \dfrac{1}{16} - \dfrac{1}{48}$

$\sf\dfrac{1}{y} = \dfrac{3-1}{48}$

$\sf \dfrac{1}{y} = \dfrac{2}{24}$

$\sf \dfrac{1}{y} = \dfrac{1}{12}$

y = 12 days