Question : A can do a piece of work in 10 days. B can do it in 15 days. With the assistance of C, they completed the work in 5 days. How many days C alone can do it?
Option 1: 20
Option 2: 25
Option 3: 30
Option 4: 35
Correct Answer: 30
Solution :
Time taken by A alone to do the work = 10 days
Part of work done by A in a day = $\frac{1}{10}$
Time taken by B alone to do the work = 15 days
Part of work done by A in a day = $\frac{1}{15}$
Part of work done by A and B in 5 days = 5 × ($\frac{1}{10}+\frac{1}{15}$) = 5 × ($\frac{3+2}{30}$) = $\frac{25}{30}$
Part of work done by C in 5 days = 1 – $\frac{25}{30}$ = $\frac{5}{30}$
Part of work done by C in a day = $\frac{1}{30}$
$\therefore$ Time taken by C alone to do the work = (1 ÷ $\frac{1}{30}$) = 30 days
Hence, the correct answer is 30.
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