Question : P, Q, and R can do a piece of work in 60 days, 100 days and 80 days respectively. They together work to finish the work and receive Rs. 2256. Then, P will get ___.
Option 1: Rs. 576
Option 2: Rs. 752
Option 3: Rs. 960
Option 4: Rs. 564
Correct Answer: Rs. 960
Solution :
Given: P, Q and R can do a piece of work in 60 days, 100 days, and 80 days.
The total work of P, Q, and R is LCM of (60, 100, 80) = 1200 units
One day's work of P $=\frac{1200}{60}=20$
One day's work of Q $=\frac{1200}{100}=12$
One day's work of R $=\frac{1200}{80}=15$
The amount will be divided among P, Q, and R as per the ratio of the work done in 1 day.
The ratio of 1 day's work of P, Q, and R = 20 : 12 : 15
The amount received by P $=\frac{20}{20+12+15}\times 2256=\frac{20}{47}\times 2256 =960$
Hence, the correct answer is Rs. 960.
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