Question
'Manoj' can complete some work alone in 40 days. 'Sohan'
is twice as efficient as 'Rohan' and five times as efficient as 'Manoj'. If 'Manoj' and 'Rohan' start working together, then after how many days should 'Sohan' replace them so that the work gets completed in exactly 15 days?Solution
ATQ, Let the total work be 120 units. Efficiency of 'Manoj' = 120 ÷ 40 = 3 units/day Efficiency of 'Sohan' = 5 X 3 = 15 units/day Efficiency of 'Rohan' = 15 ÷ 2 = 7.5 units/day Let the number of days for which 'Sohan' worked alone be 'd'. So, (d X 15) + (15 - d) X (3 + 7.5) = 120 Or, 15d + 157.5 - 10.5d = 120 Or, 'd' = 6 So, 'Sohan' worked alone for 6 days 'Sohan' should've joined them after (15 - 6) = 9 days
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