Multiple choice

A can complete a work in 12 days and B can complete the same work in 18 days. A and B start the work together, but after 4 days, A leaves the work. C then joins B and together they finish the remaining work in 5 days. If the total wages paid for the work is ₹7200 and wages are divided in proportion to the work done, what is C's share of the wages?

  1. ₹1675

  2. ₹1079

  3. ₹1200

  4. ₹1145

  5. ₹1935
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = 1/12, B's rate = 1/18. A and B work for 4 days: 4 * (1/12 + 1/18) = 4 * (5/36) = 5/9. Remaining work = 4/9. B and C do this in 5 days: 5 * (1/18 + C_rate) = 4/9. 1/18 + C_rate = 4/45. C_rate = 4/45 - 1/18 = (8-5)/90 = 3/90 = 1/30. Total work done by C = 5 * (1/30) = 5/30 = 1/6. C's share = (1/6) * 7200 = 1200.

AI explanation

Assume the total work is the least common multiple of 12 and 18, which is 36 units, making A's rate 3 units per day and B's rate 2 units per day. In the first 4 days, A and B complete 4 * (3 + 2) = 20 units, leaving 16 units of work. B works for 5 more days with C, completing 5 * 2 = 10 units, so C must complete the remaining 6 units in those 5 days. The total wage of 7200 is divided by the 36 total units to get 200 per unit, making C's share for 6 units equal to 1200.

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