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Question:

Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is

Explanation:

Let work done per day (efficiency) of Gautam and Suhani are 'g' and 's' units.

A shortfall of 40% for Gautam is compensated by 50% extra work done by Suhani.
⇒ 0.4 × g = 0.5 × s
⇒ g/s = 5/4
⇒ Let g = 5x and s = 4x

Together they can complete the work in 20 days.
⇒ Total work to be done = 20 × (5x + 4x) = 180x units

The faster among the two is Gautam whose efficiency is 5x.

∴ Time required by Gautam alone = 180x / 5x = 36 days.

Hence, 36.

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