Question

A water tank with a capacity of 500 gallons of water is filled up to two-fifth of the tank. There were two pipes, A and B, to fill the tank. Pipe A can fill the tank in 10 minutes, whereas pipe B can fill it in 6 minutes.

If Macey opens both the pipes to fill the tank, then how long will it take to fill the tank completely?

• A. $\frac{15}{4}\text{minutes}$
• B. $\frac{15}{2}\text{minutes}$
• C. $\frac{13}{4}\text{minutes}$
• D. $\frac{11}{4}\text{minutes}$

Answer 1

The correct option is A $\frac{15}{4}\text{minutes}$

Capacity of the tank = 500 gallons

Volume of the tank already filled with water $=\frac{2}{5}\times 500$
= 200 gallons

Remaining capacity of the tank to be filled with water
= 500 – 200 gallons
= 300 gallons

Time taken by pipe A to fill the tank = 10 minutes

Time taken by pipe B to fill the tank = 6 minutes

Capacity of the tank filled in 1 minute by $\text{both the pipes}=\frac{Totalcapacitytobefilled}{Totaltimetakentofill}$

Capacity of the tank filled by pipe A in 1 $\text{minute}=\frac{300}{10}=30\text{gallons}$

Capacity of tank filled by pipe B in 1 $\text{minute}=\frac{300}{6}=50\text{gallons}$

∴ Capacity of the tank filled in 1 minute by pipe A and pipe B = 30 + 50
= 80 gallons

Time taken to fill 300 gallons = $\frac{Capacitytobefilled}{Capacityofthetankfilledin1minute}$

$=\frac{300}{80}$

$=\frac{15}{4}\text{minutes}$

Thus, pipes A and B take $\frac{15}{4}$ minutes to fill 300 gallons of water in the tank.