Question : Jason can do a piece of work alone in 23.4 days, while Rafique can do the same piece of work alone in 39 days. In how many days can the duo, complete the same work if they work together?
Option 1: 14.750
Option 2: 14.625
Option 3: 14.875
Option 4: 14.375
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Correct Answer: 14.625
Solution :
Time taken by Jason alone to complete the work = 23.4 days
⇒ Part of work done by Jason alone in a day = $\frac{1}{23.4}$ = $\frac{10}{234}$
Time taken by Rafique alone to complete the work = 39 days
⇒ Part of work done by Rafique alone in a day = $\frac{1}{39}$
Let the time taken by Jason and Rafique together to complete the work = $x$ days
⇒ Part of work done by Jason and Rafique in a day = $\frac{1}{x}$
According to the question,
$\frac{10}{234}$ + $\frac{1}{39}$ = $\frac{1}{x}$
$⇒\frac{1}{x}$ = $\frac{10+6}{234}$= $\frac{8}{117}$
$⇒x$ = $\frac{117}{8}$ = 14.625
Hence, the correct answer is 14.625.
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