Question
Download Solution PDFM can do a piece of work in 12 days and N in 24 days. They begin together, but M leaves the work 6 days before the completion of the work. Find the total number of days to complete the entire work.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
M can do the work in 12 days.
N can do the work in 24 days.
M leaves 6 days before completion.
Concept/Formula used:
Work done = Efficiency × Time.
Efficiency here is the amount of work done by M and N in one day.
Solution:
Calculate LCM of 12, 24
⇒ LCM = 24 (total work)
Efficiency of M:
⇒ 24/12 = 2 units/day
Efficiency of N:
⇒ 24/24 = 1 unit/day
Combined efficiency of M and N:
⇒ 2 + 1 = 3 units/day
Work done by N alone in the last 6 days:
⇒ 1 unit/day × 6 days = 6 units
Remaining work (done by M and N):
⇒ 24 units - 6 units = 18 units
Time for M and N to do remaining work:
⇒ 18 units ÷ 3 units/day = 6 days
Total time = 6 days (M and N together) + 6 days (N alone) = 12 days
Hence, the total time to complete the work is 12 days.
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