Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
10 min. 20 sec.
11 min. 45 sec.
12 min. 30 sec.
14 min. 40 sec.
Explanation:
Part filled in 4 minutes = 4$ \left(\dfrac{1}{15} +\dfrac{1}{20} \right) $=$ \dfrac{7}{15} $.
Remaining part =$ \left(1 -\dfrac{7}{15} \right) $=$ \dfrac{8}{15} $.
Part filled by B in 1 minute =$ \dfrac{1}{20} $
$\therefore \dfrac{1}{20} $:$ \dfrac{8}{15} $:: 1 : $ x $
$ x $ =$ \left(\dfrac{8}{15} \times 1 \times 20\right) $= 10$ \dfrac{2}{3} $min = 10 min. 40 sec.
$\therefore$ The tank will be full in $\left(4 min. + 10 min. + 40 sec.\right)$ = 14 min. 40 sec.