In what ratio must a grocer mix two varieties of tea worth Rs 60 a kg and Rs 65 a kg so that by selling the mixture at Rs 68.20 a kg, he may gain 10%.(a)  3 : 2        (b)  3 : 4       (c)  3 : 5       (d)   4 : 5Options :abcd

The grocer wants to gain 10% by selling the mixture at Rs 68.20 a kg. So, the cost price of the mixture for the grocer would be 100% if 110% is Rs 68.20.

Step 1: Find the cost price of the mixture for the grocer (100/110) * 68.20 = Rs 62/kg

Step 2: Use the rule of alligation to find the ratio in which the two varieties should be mixed. The rule of alligation states that:

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

Here, the C.P. of the cheaper variety is Rs 60/kg, the mean price is Rs 62/kg, and the C.P. of the dearer variety is Rs 65/kg.

Step 3: Substitute the values into the formula (62 - 60) : (65 - 62) = 2 : 3

So, 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 a kg. Therefore, the answer is (a) 3 : 2.

To solve this problem, we need to use 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.

Step 1: Identify the prices of the two varieties of tea and the selling price of the mixture.

The price of the first variety of tea is Rs 60 per kg. The price of the second variety of tea is Rs 65 per kg. The selling price of the mixture is Rs 68.20 per kg.

Step 2: Calculate the cost price of the mixture.

Since the grocer gains 10% by selling the mixture, the cost price of the mixture is 100% of the selling price, or Rs 68.20 / 1.10 = Rs 62 per kg.

Step 3: Use the rule of alligation to find the ratio.

The rule of alligation states that the difference between the cost price of the mixture and the price of each variety of tea, when calculated separately, gives us the ratio in which the two varieties must be mixed.

So, the difference between the cost price of the mixture and the price of the first variety of tea is Rs 62 - Rs 60 = Rs 2. The difference between the cost price of the mixture and the price of the second variety of tea is Rs 65 - Rs 62 = Rs 3.

Therefore, the two varieties of tea must be mixed in the ratio 3:2.

So, the answer is (a) 3:2.