Question

Two taps can separately fill a tank in 12 minutes and 15 minutes respectively. The tank when full can be emptied by a drain tap in 20 minutes. When the tank was empty all the three taps were opened simultaneously. In what time will the tank be filled up?

Answer 1

1^st tap can fill \(\frac{1}{12}^{th}\) tank in 1 min 2nd tap can fill \(\frac{1}{15}^{th}\) tank in 1 min 

Drain pipe drain out = \(\frac{1}{20}^{th}\) tank in 1 min 

∴ In 1 min = \(\frac{1}{12} + \frac{1}{15} - \frac{1}{20}\)

= \(\frac{15 + 12 - 9}{180} = \frac{18}{180} \)

= \(\frac{1}{10}\) of tank will get filled 

∴ The tank will get filled in 10 minutes.