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
Sita's rate = 1/20 Geeta = 3 × Sita → 3/20 Geeta = 2 × Reeta → Reeta = 3/40 Sita + Reeta = 1/20 + 3/40 = (2 + 3)/40 = 1/8 Let Geeta join after x days: Work by Sita & Reeta = x × 1/8 = x/8 Work by Geeta = (8 − x) × 3/20 Total work = 1: x/8 + (8 − x) × 3/20 = 1 → (− x + 48)/40 = 1 → x = 8 Hence, Geeta should replace them after 8 days (i.e., not needed at all)
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