In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg & Rs. 65 a kg so that by selling a mixture at Rs. 68.20 a kg, he may gain 10%?Options :3:23:43:54:5

The problem can be solved using the concept of alligation, which is a rule that allows us to find the ratio in which two or more ingredients at a given price must be mixed to produce a mixture of a desired price.

Here are the steps to solve the problem:

1. First, calculate the cost price of the mixture. Since the grocer gains 10% by selling the mixture at Rs. 68.20 per kg, the cost price of the mixture would be 100% of the price. So, 68.20/110*100 = Rs. 62 per kg.

2. Now, we can use the rule of alligation. The cost prices of the two varieties of tea are Rs. 60 per kg and Rs. 65 per kg, and the cost price of the mixture is Rs. 62 per kg.

3. Subtract the lower cost price from the cost price of the mixture, and the cost price of the mixture from the higher cost price. So, 62 - 60 = 2 and 65 - 62 = 3.

4. Therefore, the grocer must mix the two varieties of tea in the ratio 2:3 to gain 10% by selling the mixture at Rs. 68.20 per kg. So, the correct option is 2:3.