A alone can finish a work in 10 days and B alone in 15 days. Working together, they finish the work. Out of a total wage of Rs 75, what is A’s share?

Introduction / Context:
Wages are split in proportion to work done. If two workers complete a job together, each person’s share equals their rate divided by the total rate, times the total wage.

Given Data / Assumptions:

• A time = 10 days ⇒ A rate = 1/10 per day.
• B time = 15 days ⇒ B rate = 1/15 per day.
• Total wage = Rs 75.

Concept / Approach:
Share of A = (A rate / (A rate + B rate)) * total wage. This is because the entire job output is proportional to rates, not times.

Step-by-Step Solution:

Verification / Alternative check:
Check B share: (2/5) * 75 = 30. The two shares add to Rs 75 as expected.

Why Other Options Are Wrong:
Rs. 30 is B’s share; Rs. 37.50, Rs. 50, Rs. 40 are inconsistent with proportional rates.

Common Pitfalls:
Splitting wages equally; using times instead of rates; arithmetic slips converting fractions.

Final Answer:
Rs. 45