Question

A tank has three taps P, Q and R. The tap R is the tap that empties the tank. Taps P and Q have the ability to fill the tank separately in 12 minutes and 16 minutes. Shortly after opening the three taps simultaneously, tap R is closed. The tank is filled in 20 minutes. In how much time will R fill the entire tank?

Answer 1

Given :

Tap P fill the tank alone in 12 min

Tap Q fill the tank alone in 16 min

Tap R empty the tank

Total time to fill the tank = 20 min

To Find :

Time taken by Tap R alone to empty the tank

Solution :

Tap P alone time to fill the tank = $\dfrac{1}{12}$

Tap Q alone time to fill the tank = $\dfrac{1}{16}$

Let Tap R alone time to empty the tank = $\dfrac{1}{x}$

Total time taken to fill the tank when all taps open = $\dfrac{1}{20}$

According to question

Total time taken to fill the tank when all taps open = Time taken by tap P alone to fill + Time taken by tap Q alone to fill + Time taken by tap R alone to empty

i.e    $\dfrac{1}{12}$  +  $\dfrac{1}{16}$  -  $\dfrac{1}{x}$  = $\dfrac{1}{20}$

Or,   $\dfrac{1}{x}$  =  (   $\dfrac{1}{12}$  +  $\dfrac{1}{16}$ ) - $\dfrac{1}{20}$

Or,    $\dfrac{1}{x}$  =  $\dfrac{4+3}{48}$ - $\dfrac{1}{20}$

Or,     $\dfrac{1}{x}$  =  $\dfrac{7}{48}$ - $\dfrac{1}{20}$

Or,     $\dfrac{1}{x}$  = $\dfrac{ 35-12}{240}$

Or,     $\dfrac{1}{x}$  = $\dfrac{23}{240}$

Or,    x = $\dfrac{240}{23}$

Or,    x = 10 min 25 sec

Hence, Time taken by Tap R to empty the entire tank is 10 min 25 sec  . Answer