Work and Wages – Share of A from total ₹ 225 when A and B work together: A alone finishes in 3 days; B alone in 2 days. They complete the work together; total wages = ₹ 225. Find A’s share.

Introduction / Context:
Payment division for joint work is proportional to work done. For steady rates, that equals the ratio of their rates (reciprocal of times). Once the ratio is known, multiply by total wages to get each share.

Given Data / Assumptions:

• A’s time = 3 days ⇒ rate = 1/3
• B’s time = 2 days ⇒ rate = 1/2
• Total wages = ₹ 225

Concept / Approach:
Wage ratio A:B = (1/3):(1/2) = 2:3. A’s share is 2/(2+3) of the total wages.

Step-by-Step Solution:
Total ratio parts = 2 + 3 = 5A’s share = 2/5 * 225 = ₹ 90

Verification / Alternative check:
B’s share = 3/5 * 225 = ₹ 135; together ₹ 225.

Why Other Options Are Wrong:
₹ 75, ₹ 95, and ₹ 65 do not match the 2:3 split; ₹ 100 is not a 2/5 fraction of 225.

Common Pitfalls:
Using times (3:2) directly instead of reciprocal rates (2:3).

Final Answer:
₹ 90