Question : Ram can complete a piece of work in 18 days, Reena can complete the same work in 12 days, and with the help of Shyam, they finish the same work in 6 days. In how many days can Shyam alone complete the same work?
Option 1: 42 days
Option 2: 36 days
Option 3: 30 days
Option 4: 24 days
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Correct Answer: 36 days
Solution :
Time taken by Ram alone to complete the work = 18 days
⇒ Part of work done by Ram alone in a day = $\frac{1}{18}$
Time taken by Reena alone to complete the work = 12 days
⇒ Part of work done by Reena alone in a day = $\frac{1}{12}$
Let the time taken by Shyam alone to complete the work = $x$ days
⇒ Part of work done by Shyam alone in a day = $\frac{1}{x}$
Time taken by Ram, Reena and Shyam together to complete the work = 6 days
⇒ Part of work done by Ram, Reena, and Shyam in a day = $\frac{1}{6}$
So, $\frac{1}{18}+\frac{1}{12}+\frac{1}{x}=\frac{1}{6}$
$⇒\frac{1}{x}=\frac{1}{6}-\frac{2+3}{36}=\frac{1}{36}$
$\therefore x= 36$ days
Hence, the correct answer is 36 days.
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