A tank can be fully filled with water using a pipe that fills 20 liters in a minute. A bigger pipe that can fill 25 liters in a minute ..will...

Let the volume of the tank be V ( in
litres)

The rate of filling the tank with a smaller pipe is
20 L / m

Then, the time will be taker to fill the tank is 
T1 = V/20 .......(1)

Now with the bigger pipe, the rate is
25 L / m

Then the time will be taken to fill the tank is T2
= V/25

But the time taken is one minute less than the time
required to fill with smaller pipe.

==>  T2 = T1 -
1

==> T1 -1 =
v/25

==> T1 = v/25 +
1............(2)

Now from (1) and (2) we conclude
that:

v/25 + 1 = v/
20

==> (v+25) / 25 =
v/20

==> (v+25) /5  = v/
4

We will multiply by
20.

==> 4(v+25) =
5v

==> 4v + 100 =
5v

==> V = 100
litre

==> T1 = v/20 = 100/20 = 5
minutes.

Then, the time required to fill the
tank with the smaller pipe is 5 minutes.