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A and B together can do a piece of work in 10 days. A alone can do it in 30 days. The time in which B alone can do it is:
Question

A and B together can do a piece of work in 10 days. A alone can do it in 30 days. The time in which B alone can do it is:

A.

20 days

B.

15 days

C.

12 days

D.

10 days

Correct option is B

Given:

A and B together can do a piece of work in 10 days. A alone can do it in 30 days. 

Concept:

Ram is work in X days, then, 

Ram is work in one day = 1X\frac{1}{X}

solution:

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

A can alone work = 30 days

Let B can alone work = x days

130+1x=110\frac{1}{30} + \frac{1}{x} = \frac{1}{10}

1x=110130\frac{1}{x} = \frac{1}{10} - \frac{1}{30}

​​​​1x=3130\frac{1}{x} = \frac{3-1}{30}

1x=230 \frac{1}{x} = \frac{2}{30}

1x=115 \frac{1}{x} = \frac{1}{15}

x =15 days

So, The time in which B alone can do it is 15 days.

Thus, the correct answer is (b).

Alternative method:

B = 302\frac{30}{2}

B = 15 days

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