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Question:

There's a lot of work in preparing a birthday dinner. Even after the turkey is in oven, there are still the potatoes and gravy, yams, salad, and cranberries, not to mention setting the table. Three friends, Asit, Arnold, and Afzal, work together to get all of these chores done. The time it takes them to do the work together is six hours less than Asit would have taken working alone, one hour less than Arnold would have taken, and half the time Afzal would have taken working alone.

How long did it take them to do these chores working together?

Explanation:

Suppose Asit, Arnold and Afzal finish the work together in x hours.

Then Asit, Arnold and Afzal will take x + 6, x + 1 and 2x hour respectively.

$∴ \frac{1}{x + 6} + \frac{1}{x + 1} + \frac{1}{2 x} = \frac{1}{x} ∴ \frac{1}{x + 6} + \frac{1}{x + 1} = \frac{1}{2 x} \frac{x + 1 + x + 6}{(x + 6) (x + 1)} = \frac{1}{2 x} \frac{2 x (2 x + 7)}{x^{2} + 7 x + 6} = 1$

3x² + 7x – 6 = 0

(x + 3)(3x − 2) = 0

$∴ x = \frac{2}{3}$ or -3

∵ Number of hours cannot be negative.

$∴ x = \frac{2}{3}$ hr = 40 minutes

Hence, option (c).

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