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. Find the share of boy?

  1. Rs. 1500

  2. Rs. 2750

  3. Rs. 2500

  4. Rs. 2000

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

Work rates: A = 1/15, B = 1/12. Together (A+B) = (4+5)/60 = 9/60 = 3/20. With boy (A+B+Boy) = 1/5 = 4/20. Boy's rate = 4/20 - 3/20 = 1/20. Ratio of work: A:B:Boy = 1/15 : 1/12 : 1/20 = 4:5:3. Total parts = 12. Boy's share = (3/12) * 6000 = 1500.

AI explanation

Let the boy's daily work rate be represented by 1/5 - 1/15 - 1/12, since the combined rate of all three is 1/5 per day. Finding a common denominator of 60 transforms the equation to 12/60 - 4/60 - 5/60, leaving the boy's daily work rate at 3/60, or 1/20. The boy works for 5 days, completing 5/20, which is one-fourth of the total work. His share of the Rs. 6000 payment is therefore Rs. 1500.

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