Question

Two taps can fill a tank in 18 and 24 min respectively. when both the taps are opened find when the first tap be turned off so that the tank may be filled in 12 min?

Answer 1

1st tap fills the tank in 18mins ⇒ 1st tap fills T/18 of the tank in one minute

2nd tap fills the tank in 24mins ⇒ 2nd tap fills T/24 of the tank in one minute

⇒ if two taps are turned on at a time. they fill (T/18 + T/24) in 1 minute = 7T/72

suppose let the two taps are turned on up to the 12 mins then they fill 7T/6

⇒ 7T/6 can be written as T + T/6 = T + 3T/18 = T + 3(1st tap work in 1 minute)

⇒ If we turn off the 1st tap 3 minutes before the 12 mins then tank gets filled in 12 minutes.

⇒ if we turn off the 1st tap 9 minutes after both taps are turned on then the tank gets filled in 12 mins.

⇒ Answer is after 9 minutes.