EgmatQuantExpert wrote:
e-GMAT Question of the Week #24Three pipes A, B and C can fill a tank in 10, 15 and 25 minutes respectively. All the three taps are used simultaneously to fill the tank. But, due to a leak at the bottom of the tank, only \(\frac{1}{3}\)rd of the tank was filled by the time it was supposed to be full. In how much time could the leak empty a full tank?
A. \(\frac{75}{31}\)
B. \(\frac{150}{31}\)
C. \(\frac{225}{31}\)
D. \(\frac{15}{2}\)
E. \(\frac{450}{31}\)
Let \(A\), \(B\) and \(C\) be time that pipes \(A\), \(B\) and \(C\) takes to fill a tank, respectively.
We can figure out the time \(X\) that \(A\) and \(B\) take to fill a tank together using a formula \(\frac{1}{X} = \frac{1}{A} + \frac{1}{B}\).
We can figure out the time \(T\) that \(A\), \(B\) and \(C\) take to fill a tank together using a formula \(\frac{1}{T} = \frac{1}{A} + \frac{1}{B} + \frac{1}{C}\).
Then we have \(\frac{1}{T} = \frac{1}{10} + \frac{1}{15} + \frac{1}{25} = \frac{31}{150}\) or \(T = \frac{150}{31}\).
Since the tank is leaking and \(\frac{1}{3}\) of the tank was filled, the time to fill the tank is \(3T = \frac{450}{31}\).
Let \(Y\) be the sinking speed of the tank.
\(\frac{31}{150} - \frac{1}{Y} = \frac{1}{3T} = \frac{31}{450}\).
Then \(\frac{1}{Y} = \frac{31}{150} - \frac{31}{450} = \frac{62}{450} = \frac{31}{225}\)
Thus we have \(Y = \frac{225}{31}\).
Therefore, the answer is C.