Question
‘Z’ alone can complete a project in 48 days, while
‘Z’ and ‘Y’ together can finish it in 16 days. If ‘Y’ worked alone for ‘x’ days and then ‘Z’ completed the remaining work in 6 days, find the value of ‘x’.Solution
Let the total work = L.C.M of 48 and 16 = 48 units
Efficiency of ‘Z’ alone = 48 ÷ 48 = 1 unit/day
Efficiency of ‘Z’ and ‘Y’ together = 48 ÷ 16 = 3 units/day
Efficiency of ‘Y’ alone = 3 – 1 = 2 units/day According to the question,
2x + 1 × 6 = 48
Or, 2x = 48 – 6 = 42
So, x = 42 ÷ 2 = 21
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