Question : Mahesh, Suresh and Raju together can complete a work in 18 days. Mahesh and Suresh together can complete the same work in 72 days. Raju alone can finish the same work in how many days?
Option 1: 21
Option 2: 24
Option 3: 34
Option 4: 18
Correct Answer: 24
Solution :
Time taken by Mahesh, Suresh and Raju together to do the work = 18 days
Part of the work done by Mahesh, Suresh and Raju in a day = $\frac{1}{18}$
Time taken by Mahesh and Suresh together to do the work = 72 days
Part of the work done by Mahesh and Suresh together in a day = $\frac{1}{72}$
Let $x$ be the time taken by Raju to do the work.
Part of the work done by Raju in a day = $\frac{1}{x}$
$\frac{1}{72} + \frac{1}{x} = \frac{1}{18}$
⇒ $\frac{1}{x} = \frac{1}{18} – \frac{1}{72}$
⇒ $\frac{1}{x}= \frac{4-1}{72}$
⇒ $\frac{1}{x}=\frac{3}{72}$
⇒ $\frac{1}{x}= \frac{1}{24}$
⇒ $x=$ 24 days
Hence, the correct answer is 24.
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