Question
'P', 'Q', and 'R' can complete a job in 60, 90, and 120
days respectively. They begin together, but 'P' leaves 10 days before the work is done and 'Q' leaves 5 days before completion. How long did the work take? (Calculate approximate value)Solution
ATQ,
Let the total work be 360 units (LCM of 60, 90, 120)
Efficiency of 'P' = 360 / 60 = 6 units/day
Efficiency of 'Q' = 360 / 90 = 4 units/day
Efficiency of 'R' = 360 / 120 = 3 units/day
Let the time taken = n days
(6 + 4 + 3)(n - 10) + (4 + 3)(5) + 3(5) = 360
Or, 13n - 130 + 35 + 15 = 360
Or, 13n = 440
So, n = 440 / 13 = 33.84 ≈ 34 days
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