P alone can do a piece of work in 5 days and Q alone in 4 days. P and Q undertook to do it for ₹3000. With the help of R they completed the work in 2 days. How much is to be paid to R?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → ₹300
The payment is shared in the ratio of the work each person does. All three worked for the same 2 days, so first find how much of the job P and Q did; R did the rest.
Work done in 2 days:
P does \(1/5\) of the job a day: \(\displaystyle 2\times\frac{1}{5}=\frac{2}{5}\)
Q does \(1/4\) of the job a day: \(\displaystyle 2\times\frac{1}{4}=\frac{1}{2}\)
R did the part left over: \(\displaystyle 1-\frac{2}{5}-\frac{1}{2}=\frac{10-4-5}{10}=\frac{1}{10}\)
R’s share:
\(\displaystyle \frac{1}{10}\times3000=300\), that is, ₹300