P, Q and R can do a piece of work in 12 days, 15 days and 20 days respectively. They start the work together, but after 2 days P leaves; after 3 more days R leaves, and Q does the remaining work. If they get Rs 5400 for the whole work, what is Q's share?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs 3150
The money is shared in proportion to the work each person does. Taking the total work as the LCM of 12, 15 and 20, that is 60 units, makes each person's daily work a whole number.
Daily work: P \(=\frac{60}{12}=5\) units, Q \(=\frac{60}{15}=4\) units, R \(=\frac{60}{20}=3\) units
First 2 days, all three: \(2\times(5+4+3)=24\) units
Next 3 days, Q and R: \(3\times(4+3)=21\) units
Work left for Q alone \(=60-24-21=15\) units
Total work by Q \(=2\times4+3\times4+15=35\) units
Q's share \(\displaystyle =\frac{35}{60}\times5400=3150\)
Q's share is Rs 3150.