Question
'J', 'K' and 'L' can complete a task alone in 42, 21, and
14 days respectively. If 'K' and 'L' work together for 'x' days and leave, then 'J' completes the rest in 7 days. What is the value of 'x'?Solution
ATQ,
Let the total work = L.C.M of 42, 21, and 14 = 84 units
Efficiency of 'J' = 84 ÷ 42 = 2 units/day
Efficiency of 'K' = 84 ÷ 21 = 4 units/day
Efficiency of 'L' = 84 ÷ 14 = 6 units/day
Work done by 'J' in 7 days = 2 × 7 = 14 units
Work done by 'K' and 'L' in 'x' days = 84 - 14 = 70 units
So, x = 70 ÷ (4 + 6) = 7
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