Work and Wages – Split a fixed payment ₹ 900 by efficiency: A alone completes a job in 8 days; B alone in 10 days. They finish together and earn ₹ 900. Find each person’s share.

Introduction / Context:
Total wages must be split according to each worker’s contribution, which for constant rates equals the worker’s rate. The combined completion does not change the internal ratio of contributions.

Given Data / Assumptions:

• A’s time = 8 days ⇒ rate = 1/8
• B’s time = 10 days ⇒ rate = 1/10
• Total payment = ₹ 900

Concept / Approach:
Wage ratio A:B = (1/8):(1/10) = 10:8 = 5:4. Split ₹ 900 in the ratio 5:4 to get individual shares.

Step-by-Step Solution:
Total parts = 5 + 4 = 9A’s share = 5/9 * 900 = ₹ 500B’s share = 4/9 * 900 = ₹ 400

Verification / Alternative check:
Check sum: ₹ 500 + ₹ 400 = ₹ 900, as required.

Why Other Options Are Wrong:
Other splits do not match the 5:4 ratio generated by rates 1/8 and 1/10.

Common Pitfalls:
Allocating by days (8:10) instead of rates (1/8:1/10).

Final Answer:
A = ₹ 500 and B = ₹ 400