Question
Download Solution PDFA can complete a work in 12 days, B can complete the same work in 7(1/2) days, and B along with C together can complete the work in 7(1/5) days. How many days will C alone take to complete the work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFA can complete the work in 12 days.
Work rate of A = 1/12 work per day.
B can complete the work in 7(1/2) days.
Work rate of B = 1 / (15/2) = 2/15 work per day.
B + C can complete the work in 7(1/5) days.
Work rate of B + C = 1 / (36/5) = 5/36 work per day.
The work rate of C is the difference between the work rate of B + C and the work rate of B:
Work rate of C = Work rate of (B + C) - Work rate of B
Substitute the values:
Work rate of C = 5/36 - 2/15
To subtract, find a common denominator LCM of 36 and 15 = 180:
5/36 = 25/180, 2/15 = 24/180
Work rate of C = 25/180 - 24/180 = 1/180
The work rate of C is 1/180 work per day. Therefore, the time taken by C to complete the work alone is:
Time = 1/Work rate of C = 1/(1/180) = 180 days.
C alone will take 180 days to complete the work.
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