Question

Two pipes P and Q can fill a tank in 36 mins and 45 mins each. A third pipe R can empty the tank in 30 mins. Initially, P and Q are opened and after 7 mins, R is also opened. How long will it take for the tank to fill up?

• A. 30 mins
• B. 40 mins
• C. 46 mins
• D. 39 mins

Answer 1

The correct option is C

46 mins

Part filled in 7 mins = 7 ($\frac{1}{36}$ + $\frac{1}{45}$) = $\frac{7}{20}$

Remaining part = 1 - $\frac{7}{20}$ = $\frac{13}{20}$

Part filled in 1 min when P, Q and R are opened = $\frac{1}{36}$ + $\frac{1}{45}$ - $\frac{1}{30}$ = $\frac{1}{60}$

Since $\frac{1}{60}$ part is filled in 1 min.

So, $\frac{13}{20}$ part is filled in $\frac{13}{20}\times 60$= 39 min

Total time to fill the tank = 39 + 7 = 46 mins.