Three-person job completed in 5 days: A and B agree to complete a work for ₹ 600. A alone can finish in 15 days and B alone in 20 days. With the help of C, they finish in 5 days. Divide the money among A, B and C according to their work contributions.

Introduction / Context:
When a lump-sum is paid for a task completed jointly, each person's share equals their fraction of the total work. Here, A and B's individual times are given; together with C they finish in 5 days. We will compute each person's contribution and then proportionally divide ₹ 600.

Given Data / Assumptions:

• A's time = 15 days ⇒ rate = 1/15
• B's time = 20 days ⇒ rate = 1/20
• Finished with C in 5 days ⇒ total rate = 1/5
• Total payment = ₹ 600

Concept / Approach:
C's rate equals the total rate minus (A + B)'s rate. Then, each share fraction = individual rate / total rate. Multiply this fraction by ₹ 600 to get each person's amount.

Step-by-Step Solution:
Rate(A) + Rate(B) = 1/15 + 1/20 = 4/60 + 3/60 = 7/60Total rate = 1/5 = 12/60Rate(C) = 12/60 − 7/60 = 5/60 = 1/12Share fractions = (rate)/(1/5) ⇒ A = (1/15)/(1/5) = 1/3; B = (1/20)/(1/5) = 1/4; C = (1/12)/(1/5) = 5/12Amounts: A = 1/3*600 = ₹ 200; B = 1/4*600 = ₹ 150; C = 5/12*600 = ₹ 250

Verification / Alternative check:
Fractions sum: 1/3 + 1/4 + 5/12 = 4/12 + 3/12 + 5/12 = 1. Amounts add to ₹ 600. Consistent.

Why Other Options Are Wrong:
Equal split or other permutations do not match the computed contribution fractions.

Common Pitfalls:
Multiplying rates by 5 days and then re-normalizing (works too), but forgetting to divide by the total can cause errors. The fraction method is cleaner.

Final Answer:
200 , 150 , 250