Proportional wages with different working days: A, B and C agree to complete a job for ₹ 2574. They actually take different spans: A works for 8 days, B for 9 days, and C for 12 days to complete the work. Their daily wage rates are in the ratio 3 : 5 : 4. What amount should C receive?

Introduction / Context:When people work different numbers of days and their daily rates are in a given ratio, the final payment is divided in proportion to (working days) * (daily rate). This converts the ratio into actual weighted shares before splitting the lump sum.

Given Data / Assumptions:

• A, B, C work for 8, 9, 12 days respectively
• Daily wage ratio A : B : C = 3 : 5 : 4
• Total payment to divide = ₹ 2574

Concept / Approach:Let the common daily-rate unit be k. Then daily wages are 3k, 5k, 4k. Multiply by days worked to get individual shares before normalization, add them, and scale to the total amount ₹ 2574.

Step-by-Step Solution:A's share weight = 8 * 3k = 24kB's share weight = 9 * 5k = 45kC's share weight = 12 * 4k = 48kTotal weight = 24k + 45k + 48k = 117k117k = ₹ 2574 ⇒ k = 22C's amount = 48k = 48 * 22 = ₹ 1056

Verification / Alternative check:Compute A and B: A = 24*22 = ₹ 528; B = 45*22 = ₹ 990; C = 48*22 = ₹ 1056. Sum = 528 + 990 + 1056 = ₹ 2574, which matches the total.

Why Other Options Are Wrong:₹ 987 or ₹ 1035 or ₹ 1100 do not correspond to the exact 24:45:48 weighted split driven by days and rate ratio.

Common Pitfalls:Dividing merely by the 3:5:4 ratio without accounting for unequal working days; neglecting to scale to the given total after finding k.

Final Answer:₹ 1056