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 : 3:2 3:4 3:5 4:5

To solve this problem, we can use the rule of alligation which is a rule that allows us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

The rule of alligation states that:

(C.P. of cheaper - Mean Price) : (Mean Price - C.P. of dearer) = Ratio of quantities

Here, the cost price (C.P.) of the cheaper tea is Rs. 60 per kg and the cost price of the dearer tea is Rs. 65 per kg. The selling price of the mixture is Rs. 68.20 per kg, but the grocer wants a gain of 10%. Therefore, the cost price of the mixture (Mean Price) is:

Selling Price of mixture = Cost Price of mixture + 10% of Cost Price of mixture
68.20 = Cost Price of mixture + 0.10 * Cost Price of mixture
68.20 = 1.10 * Cost Price of mixture
Cost Price of mixture = 68.20 / 1.10 = Rs. 62 per kg

Now, we can apply the rule of alligation:

(C.P. of cheaper - Mean Price) : (Mean Price - C.P. of dearer) = Ratio of quantities
(60 - 62) : (62 - 65) = -2 : -3 = 2 : 3

So, the grocer must mix the two varieties of tea in the ratio 2:3 to gain a profit of 10%. Therefore, the correct option is 2:3.