Question
Time taken by 'X', 'Y' and 'Z' to finish a task is 48 days,
72 days, and 96 days respectively. All started the task together, but 'X' left 12 days before completion and 'Y' left 6 days before completion. Find the total approximate time required to finish the task.Solution
ATQ,
Let the total work be 288 units (LCM of 48, 72, and 96)
Efficiency of 'X' = 288 / 48 = 6 units/day
Efficiency of 'Y' = 288 / 72 = 4 units/day
Efficiency of 'Z' = 288 / 96 = 3 units/day
Let the work be completed in 'n' days.
Then,
(6 + 4 + 3) × (n - 12) + (4 + 3) × 6 + 3 × 6 = 288
Or, 13n - 156 + 42 + 18 = 288
Or, 13n = 384
So, n = 384 / 13 = 29.54 ≈ 30 days
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