Multiple choice

Two men undertook to do a piece of work for Rs. 6000. One alone could do it in 15 days and the other can do it in 12 days, while with the assistance of a boy, work gets completed in 5 days. What is the ratio of there work done?

  1. 2:6:7

  2. 4: 5: 3

  3. 4:8:9

  4. 3:2:8

  5. 9:7:5
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B Correct answer
Explanation

The work rates are 1/15, 1/12, and 1/5 per day. The boy's rate is 1/5 - (1/15 + 1/12) = 1/5 - 9/60 = 1/5 - 3/20 = 1/20. The ratio of their work is 1/15 : 1/12 : 1/20, which simplifies to 4:5:3.

AI explanation

The work ratio is determined by the portion of the total work each person completes in the 5-day period. The first man completes 5/15 of the work, the second man completes 5/12 of the work, and the boy completes the remaining 1 minus (1/3 plus 5/12), which equals 1/4 of the work. The ratio of their shares is (5/15) to (5/12) to (1/4), which simplifies to 4 to 5 to 3.

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