A alone can do a job in 6 days; B alone in 8 days. They agree to do it for ₹3200. With C's help, the work finishes in 3 days. How much should C be paid?

Problem restatement
Three workers complete a job in 3 days. Pay must be split proportional to individual work contributions. Find C's share.

Given data

• A's time = 6 days → a = 1/6 job/day.
• B's time = 8 days → b = 1/8 job/day.
• Total time with A, B, C together = 3 days → team rate = 1/3 job/day.
• Total payment = ₹3200.

Concept/Approach
C's daily rate = team rate − (a + b). C's work = (C's rate) × 3. Payment share ∝ work share.

Step-by-step calculation
a + b = 1/6 + 1/8 = (4 + 3)/24 = 7/24 Team rate = 1/3 C's rate = 1/3 − 7/24 = 8/24 − 7/24 = 1/24 job/day C's share of work in 3 days = 3 × (1/24) = 1/8 of the job C's payment = 1/8 × ₹3200 = ₹400

Verification
Check A's and B's shares: A's work = 3 × (1/6) = 1/2; B's = 3 × (1/8) = 3/8; C's = 1/8. Sum = 1 (complete). Payments would be ₹1600, ₹1200, ₹400 respectively, totaling ₹3200.

Common pitfalls

• Splitting payment by time instead of actual work share.

Final Answer
₹400