Work and wages sharing: A and B undertake a piece of work for a total payment of ₹ 1200. A alone can finish the work in 8 days, and B alone can finish it in 6 days. With the additional help of C, the job is completed in 3 days. Based on individual work contributions, what is C's share of the money?

Introduction / Context:
This is a classic work-and-wages allocation problem. When multiple people work together for a lump-sum amount, the distribution of money must be proportional to the amount of work each person actually does. We are given individual times (A: 8 days, B: 6 days) and the joint completion time with C (3 days). The target is C's share from ₹ 1200.

Given Data / Assumptions:

• Total job = 1 unit of work
• Rate(A) = 1/8 job per day
• Rate(B) = 1/6 job per day
• With C, job completes in 3 days ⇒ combined rate = 1/3 job per day
• Total payment to be divided = ₹ 1200

Concept / Approach:
Find C's daily rate by subtracting A and B's combined rate from the overall rate. Then compute the work C completes during 3 days. Finally, allocate the total amount in proportion to work done. Only C's portion is requested here.

Step-by-Step Solution:
Combined rate (A+B+C) = 1/3Rate(A) + Rate(B) = 1/8 + 1/6 = (3 + 4) / 24 = 7/24Rate(C) = 1/3 − 7/24 = 8/24 − 7/24 = 1/24 job per dayWork by C in 3 days = 3 * (1/24) = 1/8 of the jobC's share = 1/8 * ₹ 1200 = ₹ 150

Verification / Alternative check:
Shares by fraction: A's work = 3*(1/8) = 3/8; B's work = 3*(1/6) = 1/2; C's work = 1/8. Sum = 3/8 + 1/2 + 1/8 = 1 (consistent). Money division would be ₹ 450, ₹ 600, ₹ 150 respectively, summing to ₹ 1200.

Why Other Options Are Wrong:
₹ 450 or ₹ 300 imply C did 3/8 or 1/4 of the work, which contradicts the computed rate.₹ 100 understates C's contribution; he completes exactly 1/8 of the job.

Common Pitfalls:
Confusing time ratios with work ratios; dividing money by days instead of by work; forgetting to multiply the rate by total working days to get each person's completed fraction.

Final Answer:
₹ 150