Inferring individual daily pay from combined payouts: A, B and C together get ₹ 5400 for a work done in 36 days. A and C together get ₹ 1880 for 20 days of the same work, while B and C together get ₹ 3040 for 40 days. What is C’s daily earning?

Introduction / Context:The problem provides total payments over different durations for various combinations of workers. The key is to convert each total to a per-day amount and then set up simultaneous equations to isolate each person’s daily earning. We are asked specifically for C’s daily pay.

Given Data / Assumptions:

• (A+B+C) total = ₹ 5400 in 36 days ⇒ per day = 5400/36 = ₹ 150
• (A+C) total = ₹ 1880 in 20 days ⇒ per day = 1880/20 = ₹ 94
• (B+C) total = ₹ 3040 in 40 days ⇒ per day = 3040/40 = ₹ 76

Concept / Approach:Let a, b, c be daily earnings. Then a+b+c=150, a+c=94, b+c=76. Subtract to solve for each variable, focusing on c.

Step-by-Step Solution:From a+b+c=150 and a+c=94 ⇒ b = 150 − 94 = 56From b+c=76 ⇒ 56 + c = 76 ⇒ c = 20

Verification / Alternative check:Recover a: a = 94 − c = 94 − 20 = 74. Check sums: a+b+c = 74 + 56 + 20 = 150 — consistent.

Why Other Options Are Wrong:₹ 25, ₹ 30, ₹ 50 mismatch the linear system results; only ₹ 20 satisfies all three equations simultaneously.

Common Pitfalls:Forgetting to convert totals to per-day amounts; arithmetic slips in subtraction; mixing up variables when substituting back.

Final Answer:₹ 20