Question

Pipe X and Y take 60 minutes and 90 minutes respectively to fill a cistern. Pipe Z can empty a cistern in 60 minutes. Pipe X and Y are opened when the tank is empty. Pipe Z is opened by an attender when the tank is half full. However, one rainy day, the attender comes late and delays the opening of the Pipe Z by 9 minutes. What is the time difference of the tank overflow on that day as compared to the other days?

• A. 13 min 50 secs
• B. 13 min 30 secs
• C. 22 min 30 secs
• D. 14 minutes
• E. none ofthese

Answer 1

The correct option is B 13 min 30 secs

Option(b)

Pipe X and Y in one minute fill $\frac{1}{60}+\frac{1}{90}=\frac{1}{36}$. this means that to fill half the tank i.e. $\frac{18}{36}$, it will take 18 minutes

After half the tank in filled, all 3 taps are kept open. Pipe X and Z cancel out each other’s actions, hence only Pipe Y will be considered in filling the tank. To fill the tank Y takes 90 minutes. To fill half the tank, it will take 45 minutes. Total time taken to fill a tank on a normal day = 18+45 = 63

On the rainy day, Pipe X and Y fill for 9 minutes extra = $\frac{3}{4}$ of the tank is filled .this takes 27 minutes.

Pipe Z is opened, and Pipe Y fills for the remaining $(\frac{1}{4}{)}^{th}$ of the tank which will take $\frac{90}{4}$ = 22.5 minutes. Total time taken on a rainy day = 27+22.5 = 49.5

Time difference = 63- 49.5 = 13 min 30 secs. Option (b)