Question
'Sita' can complete some work alone in 20 days. 'Geeta'
is twice as efficient as 'Reeta' and three times as efficient as 'Sita'. If 'Sita' and 'Reeta' start working together, then after how many days should 'Geeta' replace them so that the work gets completed in exactly 8 days?Solution
ATQ, Let the total work be 60 units. Efficiency of 'Sita' = 60 Ă· 20 = 3 units/day Efficiency of 'Geeta' = 3 X 3 = 9 units/day Efficiency of 'Reeta' = 9 Ă· 2 = 4.5 units/day Let the number of days for which 'Geeta' worked alone be 'd'. So, (d X 9) + (8 - d) X (3 + 4.5) = 60 Or, 9d + 52.5 - 7.5d = 60 Or, 'd' = 3 So, 'Geeta' worked alone for 3 days 'Geeta' should've joined them after (8 - 3) = 5 days
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