Time and Work
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Q.

$A$, $B$ and $C$ can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days $A$ and $B$ left. $C$ did the remaining work (in days)

 A.

1

 B.

3

 C.

5

 D.

4

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Solution:
Option(D) is correct

If $A$, $B$ and $C$ work together for a day then they will finish

\(\left(\dfrac{1}{5}+\dfrac{1}{10}+\dfrac{1}{15}\right)^{th}\)work = \(2\times \dfrac{11}{30}=\left(\dfrac{11}{15}\right)^{th}\)work

Therefore working together for two days they will finish

$C$ alone does remain \(\left(\dfrac{11}{15}-1\right)=\left(\dfrac{4}{15}\right)^{th}\) work

But $C$ finishes \(\left(\dfrac{1}{15}\right)^{th}\)work in one day

Therefore $C$ will finish \(\left(\dfrac{4}{15}\right)^{th}\)work in 4 days.


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