Question

Anand and Bharat can cut 5 kg of wood in 20 min. Bharat and Chandra can cut 5 kg of wood in 40 min. Chandra and Anand cut 5 kg of wood in 30 min. How much time Chandra will take to cut 5 kg wood alone?

Accepted Answer

C. Let $A, B, C$ be the rate of work per minute of Anand, Bharat, and Chandra respectively to cut 5 kg of wood. $$A + B = \frac{1}{20}$$ $$B + C = \frac{1}{40}$$ $$C + A = \frac{1}{30}$$ Adding all three equations: $$2(A + B + C) = \frac{1}{20} + \frac{1}{40} + \frac{1}{30} = \frac{6 + 3 + 4}{120} = \frac{13}{120}$$ $$A + B + C = \frac{13}{240}$$ To find Chandra's rate $C$: $$C = (A + B + C) - (A + B) = \frac{13}{240} - \frac{1}{20} = \frac{13 - 12}{240} = \frac{1}{240}$$ Therefore, Chandra alone will take $240$ minutes.

Work Done by Three People Cutting Wood

Explanation

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