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Download the Free PDF of MCQs on Mixture and Alligation
Mixture and alligation problems are a type of arithmetic problem that deals with the mixing of two or more substances. The goal of these problems is to determine the proportion in which the substances should be mixed in order to obtain a desired mixture.
The alligation rule is a method for solving mixture problems. It involves creating a table with the prices of the two substances, the desired price, and the difference between the prices of the two substances. The desired price is placed in the middle of the table, and the prices of the two substances are placed on either side. The difference between the prices of the two substances is then placed below each price.
The alligation rule states that the proportion in which the two substances should be mixed is equal to the ratio of the difference between the desired price and the price of the cheaper substance to the difference between the desired price and the price of the dearer substance.
Here is an example of a mixture problem:
- A grocer wishes to sell a mixture of two varieties of pulses worth Rs. 16 per kg. The cost of one variety of pulses is Rs. 14 per kg and the other is Rs. 24 per kg. In what ratio must he mix the pulses to reach this selling price?
To solve this problem, we can use the alligation rule. We create a table with the following information:
| Price | Difference |
|---|---|
| Rs. 14 | Rs. 2 |
| Rs. 24 | Rs. 8 |
The desired price is Rs. 16, so we place this in the middle of the table. The prices of the two substances are placed on either side, and the difference between the prices of the two substances is placed below each price.
The alligation rule states that the proportion in which the two substances should be mixed is equal to the ratio of the difference between the desired price and the price of the cheaper substance to the difference between the desired price and the price of the dearer substance.
In this case, the difference between the desired price and the price of the cheaper substance is Rs. 2, and the difference between the desired price and the price of the dearer substance is Rs. 8. Therefore, the proportion in which the two substances should be mixed is 2:8, or 1:4.
Therefore, the grocer should mix the two varieties of pulses in the ratio 1:4.
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