Multiple choice

Jack and his brother Mack get a contract to dig a well and on completion, they will get Rs. 36,000. Jack alone can dig a well in 10 days, whereas his brother alone can dig the same well in 5 more days than Jack. They start digging the well with their friend Harry and complete the contract in 5 days. Find the amount (in Rs.) earned by Harry.

  1. 4,000

  2. 6,000

  3. 4,500

  4. 7,500

  5. 4,800
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Jack's rate = 1/10 per day. Mack's rate = 1/15 per day. Together with Harry (H), they finish in 5 days: 5(1/10 + 1/15 + H) = 1. So 1/10 + 1/15 + H = 1/5. H = 1/5 - 1/10 - 1/15 = (6-3-2)/30 = 1/30. Harry's share is (1/30) / (1/5) = 1/6 of the total. 36000 / 6 = 6000.

AI explanation

Using the combined work rate method, Harry's work rate is 1/5 - 1/10 - 1/15 = 1/30. The ratio of their efficiencies is the ratio of their daily work rates: Jack (1/10), Mack (1/15), and Harry (1/30), which simplifies to a 3:2:1 ratio. Harry's share of the total earnings is 1/6 of the total payment. By multiplying 1/6 by Rs. 36,000, Harry earns Rs. 6,000.

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