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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