A and B together complete a task in 24 days, Cand B together complete the same task in 18 days, and A and C together complete the task in 12 days. How many days willAtake to complete the task ifhe works alone?
Answers
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Answer:
A and B together do (1/14)th of the task in
1 day.
B and C together do (1/8)th of the task in 1
day.
A and C together do (1/7)th of the task in 1
day.
Adding all the three we get
2A+2B+2C do (1/14)+(1/8)+(1/7) =
(56+98+112)/784 = 266/784-133/392, or
A+B+C = 133/784 = 19/112
C does (19/112)-(1/14) = (19–8)/112 = 11/112th
of the work in 1 day.
A does (19/112)-(1/8) = (19–14)/112 = 5/112thof the work in 1 day.
B does (19/112)-(1/7) = (19–16)/112 = 3/112th
of the work in 1 day.
The least efficient person is B, who will
do the task, alone, in 112/3 or 37.33 days.
Next is A, who will do the task, alone, in
112/5 or 22.4 days.
C, the most efficient, will do the task,
alone, in 112/11 or 10.18 days.