☛ When we mix two or more items, we get a mixture. A mixture can have different quantities of items mixed together
☛ Let us consider an example of alcohol and water. We have 40 litres of alcohol and 10 litres of water. When we mix both of them, the resulting solution is a mixture of alcohol and water, and we have 50 l of the mixture.
☛ Suppose that we take 40 litres out of the mixture. Definitely, it will not be only alcohol. Water would also be present in the solution that is drawn out.
☛ Quantity of Alcohol : Quantity of Water = 4:1
(Since, 40 L of alcohol is mixed with 10 L of water)
This would be the ratio throughout the mixture.
This ratio would be maintained even after the 40 L of mixture is drawn out.
Hence, the quantity of alcohol in the mixture is 4/5 x 40 = 32 L
And water = 1/5 x 40 = 8 L
☛ Similarly, in the 10 L mixture that was left behind, ratio of alcohol to water is same as 4:1
Hence, the left over mixture has 8 L alcohol and 2 L water.
DETERMINING PRICE OF MIXTURE
Let us consider an example of alcohol and water. We have 40 litres of alcohol and 10 litres of water. When we mix both of them, the resulting solution is a mixture of alcohol and water, and we have 50 l of the mixture.
Assuming that the cost of alcohol as Rs. 100/litre
and the cost of water to be Rs. 0.
Total cost of the mixture
= ( 40 x 100 + 10 x 0)
Cost of the mixture per litre = 4000/50 = Rs. 80/litre
☛ Price of the mixture is known as ‘mean price’. If we see this example, the price per litre of the mixture is in between the price per litre of the items mixed ie. between Rs.100/litre (cost of alcohol) and Rs. 0/litre ( cost of water)
☛ The price of a mixture is Rs. 80 which is closer to the price of alcohol – Rs. 100 than the price of water – Rs.0
If we observe carefully,
Suppose in another experiment, 40 litres of water is added to 10 litres of alcohol,
Total cost of mixture
= 400 x 0 + 10 x 100
Cost of mixture = 1000/50
☛ In this case, cost of mixture per litre is closer to the price of water (Rs.0) than that of alcohol (Rs.100)
Replacing One liquid with Other
Another important concept in Mixture / Alligation is replacing one liquid with another.
☛ Let us say, a container contains 30 L milk and 10 L was drawn out of it and replaced with water.
Quantity after 1st operation is 30-10
= 30 x 2/3
= 20 L
After 1st operation, the quantity of milk in container is 20 L and water is 10 L.
☛ Once again the same operation was performed. 10 L of mixture was drawn and replaced with 10 L water.
The 10 L which is drawn out of mixture will contain 20/3 L of milk and 10/3 L of water and is replaced by 10 L water.
Thus effectively, milk quantity is reduced by 20/3 L and water quantity is increased by 20/3 L.
Quantity of milk after 2nd operation
= 40/3 L.
Quantity of milk after 2nd operation can also be written as,
Extending it further, quantity of milk after
3 rd operation = 30(1-1/3)3
Generalizing, whenever a liquid is replaced by another liquid,
Quantity of 1st liquid
= Q[1- Qty of 2nd liquid/Q]n
Q – Total quantity of 1st liquid initially present
n – No. of times operation is performed