Question

A,B and C together can finish a piece of work in 4 days. A alone can do the work in 12 days while C alone can do it in 10 days . How long will B take to do the work alone.

Answer 1

A alone can do it in 12 days

In 1 day, A can do = 1/12 of the work

C alone can do it in 10 days

In 1 day, C can do = 1/10 of the work

Let's say B takes b days to finish it.

In 1 day, B can do = 1/b of the work


All of them together can finish it in 4 days

So in 1 day, they all can do = 1/4 of the work

$\Rightarrow \frac{1}{12} + \frac{1}{10} + \frac{1}{b} = \frac{1}{4} \\ \\ \Rightarrow \frac{1}{b} = \frac{1}{4} - \frac{1}{12} - \frac{1}{10} \\ \\ \Rightarrow \frac{1}{b} = \frac{1 \times 15 - 1 \times 5 - 1 \times 6}{60} \\ \\ \Rightarrow \frac{1}{b} = \frac{ 15 - 5 - 6}{60} \\ \\ \Rightarrow \frac{1}{b} = \frac{4}{60} = \frac{1}{15} \\ \\ \Rightarrow b = 15 \: days$

B can do the work alone in 15 days.

Answer 2

Que:- A,B and C together can finish a piece of work in 4 days. A alone can do the work in 12 days while C alone can do it in 10 days . How long will B take to do the work alone.

Solution:-

A can do work in 12 days.

=> Work done by A in 1 day = 1/12

Let B can do work in x days.

=> Work done by B in 1 day = 1/x

Now, C can do work in 10 days.

Work done by C in 1 day = 1/10 .

A.T.Q.

$= > \frac{1}{12} + \frac{1}{10} + \frac{1}{x} = \frac{1}{4} \\ \\ = > \frac{1}{x} = \frac{1}{4} - \frac{1}{12} - \frac{1}{10} \\ \\ = > \frac{1}{x} = \frac{15 - 5 - 6}{60} \\ \\ = > \frac{1}{x} = \frac{4}{60} \\ \\ = > 4x = 60 \\ \\ = > x = \frac{60}{4} \\ \\ = > x = 15$

Therefore, B can Finish it's work in 15 days.