Question

Three pipes A, B and C can fill a tank in $6$ hours. After working at it together for $2$ hours, C is closed and A and B can fill the remaining part in $7$ hours. The number of hours taken by C alone to fill the tank is.

• A. $10$
• B. $12$
• C. $14$
• D. $16$

Answer 1

Answer: (C)

The correct option is C $14$
Part time in $2$ hours$=\frac{2}{6}=\frac{1}{3}$
Remaining part$=\left(1-\frac{1}{3}\right)=\frac{2}{3}$.
$\therefore (A+B)$'s $7$ hour's work$=\frac{2}{3}$
$(A+B)$'s $1$ hour's work$=\frac{2}{21}$
$\therefore$ C's hour's work$=\left\{\right(A+B+C)$'s $1$ hour's work$\}-\{(A+B)$'s $1$ hour's work$\}$
$=\left(\frac{1}{6}-\frac{2}{21}\right)=\frac{1}{14}$
$\therefore$ C alone can fill the tank in $14$ hours.