Question
Download Solution PDFP and Q can complete a project in 15 days and 10 days, respectively. They started doing the work together, but after 2 days, Q had to leave and P alone completed the remaining work. In how many days was the whole work completed?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF(P + Q)'s 1 day's work = 1/15 + 1/10
⇒ (2 + 3)/30
⇒ 5/30
⇒ 1/6
Work done by P and Q in 2 days = 1/6 × 2
⇒ 1/3
Remaining work = 1 - 1/3
⇒ 2/3
Now,
1/15 work is done by P in 1 day.
So, 2/3 work will be done by P in 15 × 2/3 = 10 days
So, the total time is taken = 10 + 2
⇒ 12 days
∴ The whole work was completed in 12 days.
Alternate MethodCalculation:
LCM of 15, 10 is 30
Efficiency of P = 30/15 = 2
Efficiency of Q = 30/10 = 3
Two days of work will be (2 + 3) × 2 = 10
Remaining work = 30 - 10 = 20
As Q left remaining work will be done by P = 20/2 = 10 days
Total work done in 10 + 2 = 12 days
Last updated on Jul 7, 2025
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