Question
'X', 'Y', and 'Z' can complete a job individually in 20
days, 30 days, and 24 days respectively. 'Y' and 'Z' begin the task together. After 6 days, 'Z' leaves and 'X' joins 'Y' to finish the job. Determine the total number of days required to complete the task.Solution
ATQ,
Let the total work be 120 units (LCM of 20, 30, and 24)
Efficiency of 'X' = 120 ÷ 20 = 6 units/day
Efficiency of 'Y' = 120 ÷ 30 = 4 units/day
Efficiency of 'Z' = 120 ÷ 24 = 5 units/day
Let the total time taken be T days.
So, (4 + 5) × 6 + (6 + 4) × (T − 6) = 120
⇒ 54 + 10(T − 6) = 120
⇒ 54 + 10T − 60 = 120
⇒ 10T = 126
⇒ T = 12.6 days
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