Multiple choice

A and B undertook to complete a piece of work for Rs. 4500. A can do it in 12 days, B can do it in 16 days and with the help of C, they complete the work in 5 1/3 days. Find the share of C?

  1. Rs. 850

  2. Rs. 1000

  3. Rs. 600

  4. Rs. 700

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1/12, B's rate = 1/16. A+B+C rate = 1 / (16/3) = 3/16. C's rate = 3/16 - 1/12 - 1/16 = 2/16 - 1/12 = 1/8 - 1/12 = (3-2)/24 = 1/24. Share is proportional to work done. C's work = (1/24) / (3/16) = (1/24)*(16/3) = 2/9. Share = 4500 * 2/9 = 1000.

AI explanation

Using the LCM method, let the total work be 48 units, making the daily work of A and B equal to 4 units and 3 units respectively. Working together with C, they complete 48 units in 16/3 days, meaning their combined daily work is 48 divided by 16/3, which equals 9 units. C's daily work is 9 minus 7, resulting in 2 units. The ratio of their efficiencies is 4:3:2, so C's share of the total Rs. 4500 is 2/9 of 4500, which equals Rs. 1000.

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