Riya mixes three varieties of Millets M1, M2 and M3 priced at Rs. 74 per kg, Rs. 68 per kg, and Rs. 63 per kg in the ratio of 1 : 2 : 4. She added some more quantity of M1 to 4 kg of this mixture. She sold this new mixture for Rs. 84 per kg, thereby making a profit of 20%. How much quantity of M1 did she mix with the mixture?

By the method of weighted average, the 7 parts (1 + 2 + 4) of the millet mixture have a price of 74 + 136 + 252, which totals Rs. 462 per 7 kg. This equals a cost price of Rs. 66 per kg for the initial mixture. For the new mixture to be sold at Rs. 84 per kg at a 20 percent profit, its cost price must be 84 divided by 1.2, which is Rs. 70 per kg. Using alligation between the initial mixture at Rs. 66 per kg and the added M1 at Rs. 74 per kg to reach Rs. 70 per kg gives a ratio of 4 to 4, or 1 to 1. Because the initial mixture used is 4 kg, the quantity of M1 added is 4 kg.

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