A grocer mixed two varieties of coffee seeds, the cost prices of which are $12.50$ and Rs. $8$ per kg. respectively. He gains $20\%$ by selling a kg. of the mixture at Rs. $12$/-. The proportion in which he has mixed the two varieties is

The selling price of the mixture is Rs. 12 per kg at a 20 percent gain, so using the cost price formula Selling Price divided by 1.2 gives the average cost price of Rs. 10 per kg. Using the rule of alligation, the ratio of the quantity of the Rs. 12.50 variety to the Rs. 8 variety is (10 minus 8) to (12.50 minus 10). This simplifies to 2 divided by 2.5, which gives the proportion 4:5.

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