Question
Download Solution PDFP takes twice as long as Q or three times as long as R to complete a task. If they work together, they can complete the task in two days. How long will it take Q to complete the task on his own?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Time taken by P = Twice the time taken by Q
Time taken by P = Thrice the time taken by R
Formula used:
Efficiency = Total work/Time taken
Calculation:
Let the time taken by P be 6 units
⇒ Time taken by Q = 3 units
⇒ Time taken by R = 2 units
L.C.M of (2, 3 and 6) = 6 units (Total work)
⇒ Efficiency of P = 6/6 = 1 units/day
⇒ Efficiency of Q = 6/3 = 2 units/day
⇒ Efficiency of R = 6/2 = 3 unit/day
Total efficiency = (1 + 2 + 3) = 6 units/day
They complete the task in 2 days,
Hence, total units of work = 6 × 2 = 12 units
Thus, Q takes total time,
⇒ 12/2 = 6 days
It takes 6 days for Q to complete the task on his own.
Shortcut Trick
We know time is inversely proportional to efficiency.
So Ratio of efficiency
⇒ P : Q : R = 1 : 2 : 3
Total work in 2 days = 12
Time take by Q = 12/2 = 6 days
Last updated on Jul 19, 2025
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