Final answer:
The wages paid to Q for completing the work are Rs. 200. This is calculated based on the work contributions of P, Q, and R, with Q being responsible for 1 out of a total of 10 units of work when P and R's contributions are also considered.
Step-by-step explanation:
The student has provided us with the information that P, Q, and R can complete a piece of work together in 4 days. P alone can complete the work in 8 days, and R alone can complete it in 10 days. The total wages for the work are Rs.2,000, and we need to find out how much Q should be paid for their share of the work.
Firstly, we need to calculate the work contribution of P and R when they work alone. P's work rate is (1 work)/8 days, and R's work rate is (1 work)/10 days. In a set of common days, which we take as the LCM of 8 and 10, being 40 days, P would complete 5 pieces of the work and R would complete 4 pieces of the work.
When P, Q, and R work together, they finish 1 work in 4 days, which means they can complete 10 works in 40 days. Therefore, all three combined earn Rs.2,000 for these 10 pieces of work.
To find out Q's share, we subtract P and R's work contributions from the total work done:
Total work done by P, Q, and R together: 10 works (in 40 days)
Total work done by P alone: 5 works (in 40 days)
Total work done by R alone: 4 works (in 40 days)
Thus, work done by Q alone: 10 - (5 + 4) = 1 work (in 40 days).
Since Q completes 1 out of 10 works, Q should receive 1/10th of the total wages, which is Rs.2,000 * (1/10) = Rs. 200.