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Raman is three times as efficient as Manan. Raman can complete a work in 60 days less than Manan. In how many days the work would be complete if both of them work together?

Raman is three times as efficient as Manan. Raman can complete a work in 60 days less than Manan. In how many days the work would be complete if both of them work together? Correct Answer 22.5

Let the work done by Raman be x

Then work done by Manan will be 3x

Let the time taken by Manan be a days

Then Raman will complete the work in a - 60 days

So According to Work theorem

M1W2 = M2W1

⇒ x ⨯ a = 3x ⨯ (a - 60)

⇒ ax = 3xa - 180x

⇒ ax( 1 - 3) = -180x

⇒ a = 90

Time taken by Manan = 90 days

Time taken by Raman = 90 - 60 = 30 days

Time taken by both to complete the work = (1 / 90) + (1 / 30)

Time taken by both to complete the work = (1 + 3) / 90

Time taken by both to complete the work = 4 / 90

Time taken by both to complete the work = 2 / 45

∴ Time taken by both to complete the work = 22.5 days

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