Work and Wages – Contract of ₹ 1100 with partial work share known: P, Q, and R take a job for ₹ 1100. P and Q together are supposed to do 7/22 of the work. How much should R receive?

Introduction / Context:
Lump-sum contracts are split by fractional contributions to total work. If a group’s share of work is known, the remainder belongs to the other party, who then earns the corresponding share of the payment.

Given Data / Assumptions:

• Total payment = ₹ 1100
• P + Q together do 7/22 of the work
• R does the remainder

Concept / Approach:
R’s work fraction = 1 − 7/22 = 15/22. Therefore, R’s money share is the same fraction of the total amount.

Step-by-Step Solution:
R’s share = (15/22) * 1100 = 15 * 50 = ₹ 750

Verification / Alternative check:
P+Q’s share would be (7/22)*1100 = ₹ 350. Sum: ₹ 350 + ₹ 750 = ₹ 1100.

Why Other Options Are Wrong:
₹ 350 is P+Q’s combined share, not R’s; other values do not match 15/22 of ₹ 1100.

Common Pitfalls:
Confusing “P and Q are supposed to do 7/22” with “they did 7/22 of the time”; here we split money by work fractions.

Final Answer:
₹ 750