In what ratio should two varieties of sugar at Rs.36 per kg and Rs.48 Kg be mixed together to get a mixture whose cost is Rs.40 per kg ?

To find the ratio in which the two varieties of sugar should be mixed, we can use the rule of alligation. The rule of alligation allows us to find the ratio in which two or more ingredients at a given price should be mixed to produce a mixture of a desired price.

Here are the steps:

1. Write down the cost of the cheaper variety and the cost of the dearer variety. In this case, Rs.36 per kg and Rs.48 per kg respectively.

2. Write down the mean price. The mean price is the cost of the mixture, which is Rs.40 per kg.

3. Calculate the differences between the mean price and the costs of the cheaper and dearer varieties. Subtract the cost of the cheaper variety from the mean price and the mean price from the cost of the dearer variety.

   Rs.40 - Rs.36 = Rs.4 Rs.48 - Rs.40 = Rs.8

4. The ratio in which the two varieties should be mixed is the inverse of these differences. So, the two varieties should be mixed in the ratio of 8:4 or simplified to 2:1.

So, the two varieties of sugar should be mixed in the ratio 2:1 to get a mixture whose cost is Rs.40 per kg.