PROBLEM ON MIXTURE AND ALLIGATION TYPE 1: USING WEIGHTED AVERAGE

The concept of weighted average is useful when a different part of the group have the same property but the proportion of each part is different. In such a case, the proportion of each part to the whole has to be factored in while finding out the average value of the attribute or property. For instance, if a milkman mixes the 2 litres of milk costing Rs. 6 per litre and 1 litre of milk costing rs. 9 per litre, then the average cost the mixture to be calculated using weighted averages.

Here the attribute is the cost and weight is the quantity of milk.

Cost of mixture = = Rs. 7 per litre.

Points to remember:

If the equal weights of two equal types of milk are mixed, the price of the mixture will be Rs. 7.50. This can be calculated by finding the simple average.
The attribute should all be of the same unit. Similarly, the weights should also be of the same

Question 1. A vessel is filled with liquid, which is 3 parts water and 5 parts milk. How much of the liquid should be drawn off and replaced by water to make it half water and half milk?

Solution: Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

water in new mixture =(3-3x/8+x) syrup in new mixture =(5-5x/8)

Then (3-3x/8+x) = (5-5x/8)

5x + 24 = 40 – 5x

10x=16==>x=8/5

So part of mixture replaced is 8/5*1/8=1/5

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