Question : A and B can do a piece of work in 15 days. B and C can do similar work in 12 days and C and A in 10 days. How many days will A take to do the work by himself?
Option 1: 13
Option 2: 24
Option 3: 40
Option 4: 8
Correct Answer: 24
Solution :
Given: A and B can do a piece of work in 15 days. B and C can do similar work in 12 days and C and A in 10 days.
(A+B) in 1 day can do $\frac{1}{15}$ part of the work.
(B+C) in 1 day can do $\frac{1}{12}$ part of the work.
(C+A) in 1 day can do $\frac{1}{10}$ part of the work.
Now (A+B+C) in 1 day can do $\frac{1}{2}×(\frac{1}{15}+\frac{1}{12}+\frac{1}{10})$ part of the work,
= $\frac{1}{2}×(\frac{15}{60})=\frac{1}{8}$ part of the work.
Therefore, A alone in 1 day can do $(\frac{1}{8}–\frac{1}{12})=\frac{1}{24}$ part of the work.
So, A alone can do the whole work in $(1÷\frac{1}{24})$ = 24 days
Hence, the correct answer is 24 days.
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