Question

A water tank can be filled by a tap in $6$ hours while it can be emptied by another tap in $8$ hours. If both the taps are opened simultaneously then after how much time will the tank get filled ?

• A. $14$ hours
  
• B. $32$ hours
• C. $18$ hours
• D. $24$ hours

Answer 1

Answer: (D)

$24$ hours

Let L be the capacity of tank in liters.
Tank will be filled at the rate $\frac{L}{6}$ liters\hour.
While, The tank will get emptied at the rate $\frac{L}{8}$ liters\hour.
$\therefore$ Effective rate of filling the tank is $\frac{L}{6}-\frac{L}{8}=\frac{L}{24}$ liters/hour.
$\therefore$ The tank will get filled in $L\times \frac{24}{L}=24$ hours.