Question
Download Solution PDFA completes 2/3 of a certain job in 6 days. B can complete 1/3 of the same job in 8 days and C can complete 3/4 of the work in 12 days. All of them work together for 4 days and then A and C quit. How long will it take for B to complete the remaining work alone?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A completes 2/3 of a job in 6 days.
B completes 1/3 of the job in 8 days.
C completes 3/4 of the job in 12 days.
Formula Used:
Work done per day = Total work / Number of days.
Calculation:
We can find total work done by A, B & C in total days form, by cross method one by one.
A completes 2/3 of a certain job in 6 days.
A can complete total part of the work = 3 × 6/2 = 9 days.
Similarly,
B can complete 1/3 of the same job in 8 days.
B can complete total part of the work = 3 × 8 = 24 days.
C can complete 3/4 of the work in 12 days.
C can complete total part of the work = 4 × 12/3 = 16 days.
Total work = LCM of (9, 24, & 16) = 144 units.
Efficiency of A = 144/9 = 16 units, Efficiency of B = 144/24 = 6 units, Efficiency of C = 144/16 = 9 units.
All of them work together in 1 days (16 + 6 + 9) = 31 units
All of them work together for 4 days = 31 × 4 = 124 units
Efficiency of B = 6 units
Remaining work done by B = (144 - 124)/ 6 units
Remaining work done by B = 20 / 6 = 3.33 days.
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