Question : A and B can do a piece of work in 10 days. B and C can do it in 12 days. C and A in 15 days. In how many days will C finish it alone?
Option 1: 24 days
Option 2: 30 days
Option 3: 40 days
Option 4: 60 days
Correct Answer: 40 days
Solution :
Given: A and B can do a piece of work in 10 days.
B and C can do it in 12 days.
C and A can do it in 15 days.
1 day work of A and B = $\frac{1}{10}$ -------(1)
1 day work of B and C = $\frac{1}{12}$ ------(2)
1 day work of A and C = $\frac{1}{15}$ ------(3)
Adding equations (1), (2), (3), we have:
2 × (A + B + C)'1 day work = $\frac{1}{10}+\frac{1}{12}+\frac{1}{15}$
⇒ 2 × (A + B + C)'s 1 day work = $\frac{6+5+4}{60}=\frac{1}{4}$
⇒ (A + B + C)'s 1 day work = $\frac{1}{8}$
1 day work of C = 1 day's work of (A + B + C) – 1 day's work of A and B = $\frac{1}{8}-\frac{1}{10}$
1 day work of C = $\frac{5–4}{40}=\frac{1}{40}$
So, C alone will finish the work in 40 days.
Hence, the correct answer is 40 days.
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