Question
‘P’, ‘Q’ and ‘R’ can finish a task in 12
days, 36 days and 72 days respectively. ‘P’ and ‘Q’ begin the task. After ‘n’ days, ‘P’ leaves and ‘R’ joins ‘Q’. If the total work is completed in 20 days, find the value of 2n.Solution
ATQ,
Let the total work be 72 units (LCM of 12, 36, 72) Efficiency of ‘P’ = 72 / 12 = 6 units/day Efficiency of ‘Q’ = 72 / 36 = 2 units/day Efficiency of ‘R’ = 72 / 72 = 1 unit/day ATQ, (6 + 2) × n + (2 + 1) × (20 - n) = 72 Or, 8n + 3(20 - n) = 72 Or, 8n + 60 - 3n = 72 Or, 5n = 12 Or, n = 2.4 Required value = 2 × 2.4 = 4.8
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