Workers A, B, and C can complete a piece of work alone in 8 days, 10 days, and 12 days respectively. If all three work together on the job and they receive a total payment of Rs 7400 for completing it, what is the share (in rupees) of worker B, assuming the payment is divided in proportion to the amount of work each does?

Introduction / Context:
This problem combines time and work concepts with proportional division of money. Workers A, B, and C each have different times to complete the same task individually. When they work together and receive a total payment, it is fair to distribute the money in proportion to the work contributed by each worker. The question asks specifically for B's share of the total payment.

Given Data / Assumptions:

• A alone completes the work in 8 days.
• B alone completes the work in 10 days.
• C alone completes the work in 12 days.
• Together, they complete one whole job and are paid Rs 7400.
• The payment is distributed in proportion to the amount of work each worker performs.
• Total work is considered as 1 unit.

Concept / Approach:
Since payment is proportional to work contribution, we first determine the daily work rate of each worker. If a worker completes a job in T days, then his rate is 1/T units per day. When they work together for the time necessary to complete one job, each person's contribution to the total work will be proportional to their rate. Therefore, the ratio of their rates equals the ratio of their shares of the total money.

Step-by-Step Solution:
Step 1: Let total work be 1 unit. Step 2: A's rate = 1/8 units per day. Step 3: B's rate = 1/10 units per day. Step 4: C's rate = 1/12 units per day. Step 5: Combined rate of A, B, and C = 1/8 + 1/10 + 1/12. Step 6: Find common denominator. The least common multiple of 8, 10, and 12 is 120. Step 7: Convert each rate: 1/8 = 15/120, 1/10 = 12/120, 1/12 = 10/120. Step 8: Combined rate = 15/120 + 12/120 + 10/120 = 37/120 units per day. Step 9: Time to complete the work together = 1 / (37/120) = 120/37 days (this time is not directly needed for share calculation but confirms they finish the job). Step 10: The share ratio of A : B : C equals their rates 1/8 : 1/10 : 1/12, that is 15/120 : 12/120 : 10/120, which simplifies to 15 : 12 : 10. Step 11: Sum of ratio parts = 15 + 12 + 10 = 37. Step 12: B's share of the total payment = (12 / 37) * 7400. Step 13: Compute B's share: 7400 / 37 = 200, then 200 * 12 = 2400.

Verification / Alternative check:
We can check by finding the other shares. A's share = (15/37) * 7400 = 15 * 200 = 3000. C's share = (10/37) * 7400 = 10 * 200 = 2000. Adding them yields 3000 + 2400 + 2000 = 7400, which matches the total payment. This confirms that the allocation is consistent and correct.

Why Other Options Are Wrong:

• 2600: This value does not correspond to the correct proportional ratio of 15:12:10.
• 3000: This is actually A's share, not B's.
• 2000: This is C's share, which is lower than B's because C is slower than B.

Common Pitfalls:
A common mistake is to treat the days directly as the ratio for sharing money instead of using work rates. Remember that a smaller number of days means a higher rate, so the share must be proportional to 1/T, not T itself. Another error is to ignore simplification of fractions, which can lead to complicated numbers; using a common denominator helps to see simple integer ratios.

Final Answer:
Worker B's share of the payment is Rs 2400.