If A had worked alone, he would have taken 63 hours to complete a task. However, A and B together complete this task in 36 hours and receive Rs 5,950 as total payment. Assuming that the wages are shared in proportion to the work done by each, what is B's share of the total payment?

Introduction / Context:

Here, time and work concepts are tied directly to wage distribution. The problem asks us to use the given individual and combined completion times to determine how much of the total work B performs, and from that, how much of the total payment is due to B. This situation often appears in questions where fairness of payment is based on actual contribution rather than equal splitting.

Given Data / Assumptions:

• A alone would complete the task in 63 hours.
• A and B together complete the same task in 36 hours.
• Total payment for the completed task is Rs 5,950.
• Payment is shared in proportion to the work done by each worker.
• Work rate is constant over time, and total work is considered as one unit.

Concept / Approach:

The idea is to turn completion times into hourly work rates. The combined rate of A and B can be compared with A's individual rate to find B's rate. After finding individual rates, we compute how much of the total job B actually completes during the 36 hours. This fraction of the total work equals the fraction of the total wages that B should receive, since wages are proportional to contribution.

Step-by-Step Solution:

Verification / Alternative Check:

A's share would be 4/7 of 5,950, which is 3,400. Adding A's share and B's share gives 3,400 + 2,550 = 5,950, which matches the total amount. Also, the work fractions 4/7 and 3/7 sum to 1 unit of work, confirming that our rates correctly describe the contributions of A and B over 36 hours.

Why Other Options Are Wrong:

A share of 3,400 or 3,600 would assign B more work than he actually did relative to A. Likewise, 2,750 would not maintain the 4 : 3 ratio implied by the work done. Only Rs 2,550 fits both the work ratio and the total payment constraint and is consistent with the derived rates from the time data.

Common Pitfalls:

Some candidates assume the payment should be divided in the ratio of times, that is 63 : 36, instead of using the ratio of work done. Others mistakenly treat 36 hours as a fraction of only A's time without introducing B's contribution correctly. Always remember that wage distribution in such problems is based on the amount of work done, not on the time spent alone or combined.

Final Answer:

B's correct share of the total payment is Rs 2,550.