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Q)

'A' alone can do a certain job in 15 days while B alone can do it in 10 days. 'A' started the work and was joined by B after 5 days. For how long did this work last?

Explanation

According to the question,

In 5 days A can complete$=\frac{1}{15}\times 5=\frac{1}{3}$^{rd} of the work

Remaining work $=1-\frac{1}{3}=\frac{2}{3}$

In one day (A+B) can complete$=\frac{1}{15}+\frac{1}{10}=\frac{2+3}{30}=\frac{5}{30}=\frac{1}{6}$^{th} of the work

∴ $\frac{2}{3}$^{ rd} of the work will be finished by (A+B) in $\frac{2}{3}\times 6$ days that is in 4 days.

∴ Total time taken= (5+4) days =9 days.

**Hence option D is the correct **

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