a tap can fill a tank in 15 minutes .another tap can empty it in 20 minutes.Initially the tank is empty,if both the taps start functioning the same time,when will the tank become fill?

each minute the tank

gains 1/15
loses 1/20

So, the net gain in volume is

1/15 - 1/20 = 1/60

So, it will take 60 minutes to fill up.

60 min

To determine when the tank will become full, we need to calculate how much water is being filled and how much is being emptied in a given amount of time.

Let's start by finding the rates at which each tap fills or empties the tank:

- Tap 1 fills the tank in 15 minutes, so its filling rate is 1/15 of the tank's capacity per minute.
- Tap 2 empties the tank in 20 minutes, so its emptying rate is 1/20 of the tank's capacity per minute.

Since Tap 1 is filling the tank and Tap 2 is emptying it, we can subtract the emptying rate from the filling rate to determine the net rate at which the tank is filling:

Net filling rate = (Filling rate of Tap 1) - (Emptying rate of Tap 2)
= 1/15 - 1/20
= (20 - 15) / (15 * 20)
= 1/60 of the tank's capacity per minute

Now, we can calculate how long it will take for the tank to fill completely:

Time to fill = (Tank capacity) / (Net filling rate)
= 1 / (1/60)
= 60 minutes

Therefore, it will take 60 minutes for the tank to become full if both taps start functioning at the same time.