A and B together complete three fifths of a piece of work and C alone completes the remaining part. If A, B and C receive a total payment of Rs 5000 for the entire job, what is the share of C?

Introduction / Context:
This aptitude question checks understanding of how wages or payment are distributed when different workers complete different fractions of the same job. The key idea is that money is shared in direct proportion to the amount of work done by each person.

Given Data / Assumptions:

• A and B together complete three fifths of the total work.
• C alone completes the remaining two fifths of the work.
• Total payment for the full work is Rs 5000.
• Payment is assumed to be shared in direct proportion to the fraction of work completed by each party.

Concept / Approach:
The basic concept is proportional division. If a worker completes a certain fraction of the total job, that worker is entitled to the same fraction of the total payment. Therefore, once we know what fraction of the work C completes, we can multiply that fraction by the total payment to obtain the amount due to C.

Step-by-Step Solution:
Step 1: Let the total work be 1 unit. Then the work done by A and B together is 3/5.Step 2: Since A and B together complete 3/5 of the work, the remaining work is 1 - 3/5 = 2/5 of the total.Step 3: This remaining 2/5 of the work is completed entirely by C.Step 4: Total payment for the complete work is Rs 5000.Step 5: Share of C is equal to the fraction of work completed by C multiplied by the total payment, that is (2/5) * 5000.Step 6: Compute (2/5) * 5000 = 2 * 1000 = Rs 2000.

Verification / Alternative check:
We can also find the combined share of A and B. Since they together do 3/5 of the work, their combined share is (3/5) * 5000 = 3000. Adding the share of C, which we found as 2000, gives 3000 + 2000 = 5000, which matches the total payment. This consistency check supports that the answer Rs 2000 is correct.

Why Other Options Are Wrong:

• Rs 3000: This would be the combined share of A and B for three fifths of the work, not the share of C.
• Rs 2500: This amount corresponds to half of the total payment, but C does not complete half the work. C only completes two fifths of the work.
• Rs 1500: This corresponds to three tenths of the total payment and does not match the required fraction of 2/5 of the work.

Common Pitfalls:
Students sometimes divide the payment equally among all three workers, ignoring the fact that they do not all complete equal fractions of the work. Another common mistake is to misinterpret three fifths and two fifths, or to mix up the fraction that belongs to C. Remember that payment must follow the fraction of work done when no other conditions are mentioned.

Final Answer:
C receives Rs 2000 as his share of the total payment.