P, Q and R can do a piece of work in 12 days, 18 days and 24 days respectively. They start the work together, but after 3 days P leaves; after 4 more days R leaves, and Q does the remaining work. If they get Rs 7,200 for the whole work, what is Q's share?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 3,300
The money is shared in proportion to the work each person does. Taking the total work as the LCM of 12, 18 and 24, that is 72 units, makes each person's daily work a whole number.
Daily work: P \(=\frac{72}{12}=6\) units, Q \(=\frac{72}{18}=4\) units, R \(=\frac{72}{24}=3\) units
First 3 days, all three: \(3\times(6+4+3)=39\) units
Next 4 days, Q and R: \(4\times(4+3)=28\) units
Work left for Q alone \(=72-39-28=5\) units
Total work by Q \(=3\times4+4\times4+5=33\) units
Q's share \(\displaystyle =\frac{33}{72}\times7200=3300\)
Q's share is Rs 3,300.