Question
Download Solution PDFP completes \(\frac{1}{3}\) part of a work in 15 days and Q completes the remaining work in 45 days. In how many days can they together finish the same work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
P completes (1/3) of the work in 15 days.
Q completes the remaining work (2/3) in 45 days.
Formula used:
Work done per day = Efficiency
LCM method: Total work = LCM of individual work durations.
Calculation:
P completes (1/3) of work in 15 days, so full work will take:
Total work days for P = 15 × 3 = 45 days
Q completes (2/3) of work in 45 days, so full work will take:
Total work days for Q = (45 × 3) / 2 = 67.5 days
LCM of (45, 67.5) = 135 (Assuming work units)
Efficiency of P = 135 / 45 = 3 units/day
Efficiency of Q = 135 / 67.5 = 2 units/day
Total efficiency of (P + Q) = 3 + 2 = 5 units/day
Time required to complete full work = 135 / 5
= 27 days
∴ P and Q together can complete the work in 27 days.
Last updated on Jan 23, 2025
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