Question : A and B were assigned to do a job for Rs. 1,200. Working alone, A can do it in 15 days and B, in 12 days. With the help of C, they can finish in 5 days. The share of the amount that C earns is:
Option 1: Rs. 300
Option 2: Rs. 400
Option 3: Rs. 500
Option 4: Rs. 600
Correct Answer: Rs. 300
Solution :
The time taken by A alone = 15 days
⇒ Part of the work done by A in 1 day = $\frac{1}{15}$
The time taken by B alone = 12 days
⇒ Part of the work done by B in 1 day = $\frac{1}{12}$
Let the time taken by C alone = $x$
⇒ Part of the work done by C in 1 day = $\frac{1}{x}$
The time taken by A, B, and C = 5 days
⇒ Part of the work done by A, B, and C together in 1 day = $\frac{1}{5}$
According to the question,
$\frac{1}{5}=\frac{1}{15}+\frac{1}{12}+\frac{1}{x}$
⇒ $\frac{1}{x}=\frac{1}{5}-\frac{1}{12}-\frac{1}{15}=\frac{12 – 5 – 4}{60} = \frac{1}{20}$
The ratio of the amounts A, B, and C earn $= \frac{1}{15} : \frac{1}{12} :\frac{1}{20} = 4: 5: 3$
Since total amount = 1200,
Share of the amount earned by C
= $\frac{3}{12}× 1200$
= Rs. $300$
Hence, the correct answer is Rs. 300.
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