Question : A can do a piece of work in 20 days and B in 15 days. With the help of C, they finish the work in 5 days. C can alone do the work in:
Option 1: 5 days
Option 2: 6 days
Option 3: 10 days
Option 4: 12 days
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Correct Answer: 12 days
Solution : Given: A alone can do the work in 20 days. B alone can do the work in 15 days. A, B, and C together finish the work in 5 days. Let C alone finish the work in $x$ days. As per given conditions, ⇒ $\frac{1}{5}=\frac{1}{20}+\frac{1}{15}+\frac{1}{x}$ ⇒ $\frac{1}{x}=\frac{1}{5}–\frac{1}{20}–\frac{1}{15}$ ⇒ $\frac{1}{x}=\frac{12–3–4}{60}$ ⇒ $\frac{1}{x}=\frac{5}{60}$ ⇒ $\frac{1}{x}=\frac{1}{12}$ ⇒ $x=12$ days Hence, the correct answer is 12 days.
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