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A and B can do a work in 24 days and 36 days respectively. A starts the work and B joins him after some days and they do the remaining work in 6 days. After how many days did B joined with A.

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12 days

10 days

14 days

15 days

answer is C.

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Detailed Solution

1 day work of $A = \frac{1}{24}$

1 day work of $B = \frac{1}{36}$

A and B $= \frac{1}{24} + \frac{1}{36} \Rightarrow \frac{3 + 2}{72} \Rightarrow \frac{5}{72}$

6 days work of $A & B = \frac{5}{72} \times 6 \Rightarrow \frac{5}{12}$

The work done by A alone $1 - \frac{5}{12} = \frac{7}{12}$

let Time taken by A to complete is x days

$\frac{1}{24} x = \frac{7}{12}$

x=14 days

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