A and B together can complete a work in 4 days. A alone takes 6 days less than B alone. In how many days can C alone complete the work if he is 50% more efficient than B?

Correct answer: 8

Solution

Let B take x days, so A takes x-6 days. Their combined rate is 1/4, so 1/x + 1/(x-6) = 1/4, which gives x = 12. Thus B takes 12 days, and C is 50% more efficient than B, so C's rate is 1.5/12 = 1/8 per day; hence C takes 8 days.

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