Humpty can do a piece of work in 10 days and Dumpty alone can do it in 5 days. Humpty and Dumpty undertook to do it for Rs.400. With the help of their neighbor Johnny, they finished it in 2 days. Find the share of Johnny?
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$Rs. 120$
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$Rs. 200$
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$Rs. 180$
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$Rs. 160$
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$None of these$
D
Correct answer
Explanation
Humpty's rate = 1/10, Dumpty's rate = 1/5. Together they finish in 2 days, so combined rate with Johnny = 1/2. Johnny's rate = 1/2 - (1/10 + 1/5) = 1/2 - 3/10 = 2/10 = 1/5. Johnny contributes (1/5) × 2 = 2/5 of work. Share = (2/5) × 400 = Rs. 160. Option D is correct.