Robin can complete a piece of work alone in 9 days, while Amit can complete the same work alone in 6 days. If they finish the work together and receive a total payment of Rs 2500, what is Robin's share (in rupees)?

Introduction / Context:
This is a standard time and work plus wages distribution problem. Two workers, Robin and Amit, complete a job together and earn a total amount. Since payment is usually proportional to the amount of work each person does, we must compare their work rates and then split the total payment accordingly. The question specifically asks for Robin's share of the payment.

Given Data / Assumptions:
- Robin can complete the job alone in 9 days. - Amit can complete the same job alone in 6 days. - They work together to finish the entire job. - The total payment for the completed work is Rs 2500. - Wages are distributed in proportion to the work done by each person.

Concept / Approach:
If someone can complete a job in T days, their work rate is 1 / T of the job per day. When two people work together, the fraction of work each contributes is proportional to their respective rates. The ratio of their rates gives the ratio of their shares in the total payment. Therefore, we do not need the total time taken by them together; we only need the ratio of their individual rates to divide Rs 2500 between them correctly.

Step-by-Step Solution:
Step 1: Work rate of Robin = 1 / 9 job per day. Step 2: Work rate of Amit = 1 / 6 job per day. Step 3: Ratio of their rates = (1 / 9) : (1 / 6). Step 4: Simplify the ratio: (1 / 9) : (1 / 6) = 1 / 9 * 6 : 1 / 6 * 6 = 2 : 3. Step 5: Therefore, their payment share ratio is also Robin : Amit = 2 : 3. Step 6: Total shares = 2 + 3 = 5 parts. Step 7: Value of one part = 2500 / 5 = Rs 500. Step 8: Robin's share = 2 * 500 = Rs 1000.

Verification / Alternative check:
We can confirm that Amit's share would be 3 * 500 = Rs 1500. The sum 1000 + 1500 = 2500 matches the total payment, which verifies that the ratio and distribution are correct. Since the ratio of rates is logically consistent with their individual times (the one who works faster, Amit, gets the larger share), the result makes sense.

Why Other Options Are Wrong:
Rs 1700 or Rs 1200: These amounts do not follow the 2 : 3 ratio and would not sum to Rs 2500 when combined with Amit's share if calculated from the same ratio.
Rs 1500: This would incorrectly assign the larger share to Robin, even though Amit works faster and should get a bigger share of the payment.
Rs 900: This does not fit the 2 : 3 ratio and does not lead to a correct total when paired with Amit's corresponding share.

Common Pitfalls:
Students sometimes try to use the number of days directly instead of the reciprocal rates, mistakenly using 9 : 6 instead of 1 / 9 : 1 / 6. Another common error is to assume equal sharing of money without considering different efficiencies. Always convert times to rates and then form the correct ratio to divide wages fairly.

Final Answer:
Robin's share of the payment is Rs 1000.