Worker A can finish a project alone in 15 days, whereas Worker B can complete the same project alone in 20 days. Together with Worker C, they agree to complete the task for a total payment of ₹6,000. If all three working together finish the entire project in 4 days, what is the share of payment that Worker C should receive?

The correct answer is ₹3,200.

Step 1: Understand the core concept
When workers complete a project together in the same duration, the total payment is distributed in proportion to the fraction of work each worker contributes to the total task.

Step 2: Calculate the 1-day work rates of Worker A and Worker B
Worker A can finish the whole project in 15 days alone. Therefore, A's 1-day work is:
$\frac{1}{15}$
Worker B can finish the whole project in 20 days alone. Therefore, B's 1-day work is:
$\frac{1}{20}$

Step 3: Calculate the total work done by Worker A and Worker B in 4 days
All three workers worked together for 4 days to finish the entire project.
Work completed by Worker A in 4 days =
$4\times \frac{1}{15}=\frac{4}{15}$
Work completed by Worker B in 4 days =
$4\times \frac{1}{20}=\frac{4}{20}=\frac{1}{5}$

Step 4: Find the combined work done by Worker A and Worker B
Combined work of A and B in 4 days =
$\frac{4}{15}+\frac{1}{5}=\frac{4}{15}+\frac{3}{15}=\frac{7}{15}$

Step 5: Calculate the portion of work done by Worker C
The total completed project represents 1 whole unit of work. The remaining work was done by Worker C.
Work done by Worker C =
$1-\frac{7}{15}=\frac{8}{15}$

Step 6: Calculate Worker C's payment share
Worker C receives a payment proportional to their share of the total work.
Worker C's share =
$\frac{8}{15}\times ₹6000=8\times ₹400=₹3200$
Thus, Worker C should receive ₹3,200.