# Liquid Mixture

**Liquid Mixture**

A vessel contains ‘x’ liters of liquid X.

‘y’ liters of liquid are withdrawn from the vessel and is replaced with liquid Y, then another ‘y’ liters of liquid are withdrawn from the vessel and is replaced with liquid Y and the process continues for n times.

After the nth operation

**Liquid X left in the vessel after nth operation ------------------------------------------------------ = (1- y/x )^n Initial quantity of liquid X in the vessel **

Ex: A milkman with draws 1lit of milk from a vessel containing 10 lit of pure milk and replaces it with water. Lets see how the concentration changes after each operation.

Initial amount of milk = 10 lit

After first replacement, amount of milk = 9 lit and water = 1lit

As per the formula, Amount of milk left / Initial amount of milk = 1 – 1/ 10 = 9/10 (same as above)

Second operation:

Now the vessel contains 9lt milk and 1lt water

The1 lt mixture that ‘ll taken out of the container in second operation ‘ll contain 0.1 lt of water and 0.9lt of milk and that ‘ll be replaced by 1 lt of water

So amount of milk in the mixture after second operation = 9 – 0.9 = 8.1

and amount of water in the mixture after second operation = 1 – 0.1 + 1 = 1.9 (=10-81.)

Now as per formula

Amount of milk left / Initial amount of milk = (1 – 1/10)^2

= 81/100 (same as above)

Notes:

1. Some time the amount of liquid taken out and replaced by are not same. In that case don’t use the formula. Calculate the final composition by the method explained above.

2. Solve the questions in question bank and maths forum.

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