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 take one minute less to fill the same tank. How many minutes does the smaller pipe take to fill the tank?
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Let the time taken to fill the tank with the smaller pipe be T. This pipe fills at the rate of 20 liters/ minute.
So the capacity of the tank is 20T.
The bigger pipe fills at 25 liters/ minute and takes 1 minute less.
So we have 20T / 25 = T - 1
=> 20T = 25T - 25
=> 5T = 25
=> T = 5
Therefore the smaller pipe takes 5 minutes to fill the tank.
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.
Let V be the volume of the tank in litres.
Then at the rate of 20 litre per minute the smaller pipe takes V/20 minutes.
Then the bigger pipe takes V/20-1 minutes by data which should also be equal to V/ 25 minutes.
Therefore V/20 -1 = V/25. Multiplying by 20*25 we get:
25V - 20*25 = 20 V.
So 25V- 20 V = 20*25.
5V = 20* 25.
V = 20*25/ 5 = 100 litre.
So the smaller pipe takes 100/20 = 5 minutes.
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