A, B and C contract to complete a piece of work for Rs. 440. Together, A and B are supposed to do 9/11 of the work. What should be the share of C in rupees from the total payment?

Introduction / Context:
This question tests the concept of sharing money in proportion to work done. A, B, and C together take a contract for a fixed amount. The share of work done by A and B together is known as a fraction of the total, so the remaining fraction must be done by C. Payment is then divided according to the fraction of work contributed by each party.

Given Data / Assumptions:
- Total contract amount = Rs. 440.
- A, B, and C together complete the entire work.
- A and B together are to do 9/11 of the total work.
- C therefore does the remaining part of the work.
- Payment is proportional to the amount of work done by each party.

Concept / Approach:
If A and B together complete 9/11 of the work, then the remaining 2/11 of the work must be done by C. Since money is distributed in proportion to the work done, C’s share of the total payment will be the same fraction, 2/11, of the total amount. We simply multiply the total amount by 2/11 to get the rupee share of C.

Step-by-Step Solution:
Step 1: Total work is considered as 1 unit. Step 2: A and B together are to do 9/11 of the work. Step 3: Remaining work for C = 1 - 9/11 = 2/11 of the total work. Step 4: Total payment for the work = Rs. 440. Step 5: Since payment is proportional to work done, C’s share = (2 / 11) * 440. Step 6: Compute (2 / 11) * 440 = 2 * 40 = Rs. 80.

Verification / Alternative check:
We can also compute the share for A and B together: (9 / 11) * 440 = 9 * 40 = Rs. 360. The total of C’s share and the share of A and B together is 360 + 80 = 440, which matches the full contract amount. Hence the distribution is correct and consistent.

Why Other Options Are Wrong:
- 75, 90, 100, 60: None of these correspond to the fraction 2/11 of Rs. 440. They also do not leave a correct remaining amount for A and B when subtracted from 440, so they do not maintain proportionality with the given work fraction of 9/11 for A and B.

Common Pitfalls:
Some learners confuse the fraction of work done by C (2/11) with the fraction done by A and B (9/11), or attempt to split the payment equally among A, B, and C. It is essential to remember that payment should be made directly proportional to the work contribution, not to the number of workers. Another common mistake is to miscalculate (2 / 11) * 440 by not simplifying carefully.

Final Answer:
C’s correct share from the total payment is Rs. 80.