Question : P alone can do work in 10 days, Q alone can do the same work in 15 days and R alone can do the same work in 12 days. They jointly complete the work and earn Rs. 3000. What is the share of R?
Option 1: Rs. 1200
Option 2: Rs. 800
Option 3: Rs. 1500
Option 4: Rs. 1000
Correct Answer: Rs. 1000
Solution :
Let's the rate of work for P, Q, and R as P
r
, Q
r
, and R
r
respectively.
P
r
= $\frac{1}{10}$because P can complete the work in 10 days
Q
r
= $\frac{1}{15}$because Q can complete the work in 15 days
R
r
= $\frac{1}{12}$because R can complete the work in 12 days
Ratio of their efficiency P : Q : R = $\frac{1}{10}: \frac{1}{15}: \frac{1}{12} = 6 : 4: 5$
Share of R = $\frac{5}{15}$ × 3000 = 3000 = Rs.1000
Hence, the correct answer is Rs.1000.
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