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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