Question : Stanie and Paul accept a piece of work for Rs. 28,800. Working alone, one could do it in 36 days and the other, in 48 days. With the assistance of an expert, they finish it in 12 days. How much remuneration should the expert get?
Option 1: Rs. 10,000
Option 2: Rs. 18,000
Option 3: Rs. 16,000
Option 4: Rs. 12,000
Correct Answer: Rs. 12,000
Solution :
Time taken by the first person alone = 36 days
⇒ Part of work done by the first person in a day = $\frac{1}{36}$
Time taken by the second person alone = 48 days
⇒ Part of work done by the second person alone in a day = $\frac{1}{48}$
Let the time taken by the expert alone = $x$ days
⇒ Part of work done by the expert in a day = $\frac{1}{x}$
Time taken by all three working together = 12 days
⇒ Part of work done by all three in a day = $\frac{1}{12}$
According to the question,
$\frac{1}{36}$ + $\frac{1}{48}$ + $\frac{1}{x}=\frac{1}{12}$
⇒ $\frac{1}{x}=\frac{1}{12}-\frac{1}{36}-\frac{1}{48}=\frac{12-4-3}{144}=\frac{5}{144}$
⇒ Ratio of work done by Stanie, Paul, and the expert $=\frac{1}{36}:\frac{1}{48}:\frac{5}{144} = 4:3:5$
So, the amount received by the expert $=\frac{5}{4+3+5}×28800 = 5 × 2400 =$ Rs. $12000$
Hence, the correct answer is Rs. 12,000.
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