Question

A and B can separately do a piece of work in 24 days and 16 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 3 days, then the number of days in which C alone could do the work will be?

Answer 1

Answer:     C can complete the work in 12 days.

Step-by-step explanation:

Alright, lets get started.

Given that, A and B can separately do a piece of work in 24 days and 16 days respectively.

It means, in 1 day, A can complete the part of work : $\frac{1}{24}$

It means, in 1 day, B can complete the part of work : $\frac{1}{16}$

As they both worked together for 6 days,

in 6 days, A can complete the part of work : $6*\frac{1}{24}=\frac{1}{4}$

in 6 days, B can complete the part of work : $6*\frac{1}{16}=\frac{3}{8}$

So, together they had completed the work : $\frac{1}{4}+\frac{3}{8}=\frac{5}{8}$

So remaining work will be : $1-\frac{5}{8}$

So remaining work will be : $\frac{3}{8}$

Now this remaining work is done by A and C together.

Suppose C alone can do this work in C days.

So in 3 days, A and C completed the rest work  :

$3 \times(\frac{1}{24}+\frac{1}{C})=\frac{3}{8}$

$\frac{1}{24}+\frac{1}{C}=\frac{1}{8}$

$\frac{1}{C}=\frac{1}{8}-\frac{1}{24}$

$\frac{1}{C}=\frac{1}{12}$

$C=12$

Hence C can complete the work in 12 days.   :  Answer

Hope it will help :)