Question

Pipes A and B can fill a tank in $18$ minutes and $12$ minutes respectively. If both the pipes are opened simultaneously, how long will they take to fill the tank?

• A. $30$ minutes
• B. $20$ minutes
• C. $10$ minutes
• D. $7\frac{1}{5}$ minutes

Answer 1

Answer: (D)

$7\frac{1}{5}$ minutes

Let ${}^{\prime }{V}^{\prime }$ be total volume of tank

Time taken by $A$ to fill tank $=18min$

Speed of $A=\frac{V}{18}$

Time taken by $B$ to fill tank $=12min$

Speed of $B=\frac{V}{12}$

$\therefore$ Total time taken by $A$ and $B$ to fill tank when opened

Simultaneously $=\frac{V}{(\frac{V}{12}+\frac{V}{18})}$

$=\frac{18\times 12}{30}$

Time taken $=7.2min$