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 :abc

The grocer wants to gain a 10% profit by selling the mixture at Rs 68.20 per kg. This means the cost price of the mixture should be 10% less than Rs 68.20.

Step 1: Calculate the cost price of the mixture Cost price = Selling price - Profit Cost price = Rs 68.20 - 10% of Rs 68.20 Cost price = Rs 68.20 - Rs 6.82 Cost price = Rs 61.38 per kg

Step 2: Use the rule of alligation to find the ratio The rule of alligation states that the ratio in which two ingredients should be mixed to get a mixture of a certain price is equal to the difference between the price of the mixture and the price of the cheaper ingredient to the difference between the price of the more expensive ingredient and the price of the mixture.

So, the ratio = (Cost price of mixture - Cost price of cheaper ingredient) : (Cost price of more expensive ingredient - Cost price of mixture) = (Rs 61.38 - Rs 60) : (Rs 65 - Rs 61.38) = Rs 1.38 : Rs 3.62

Step 3: Simplify the ratio To simplify the ratio, divide both sides by the smallest number, which is Rs 1.38. = 1 : (Rs 3.62 / Rs 1.38) = 1 : 2.62

Since the options are in whole numbers, round 2.62 to the nearest whole number, which is 3.

So, the grocer should mix the two varieties of tea in the ratio 1:3. However, this option is not available in the given options. There might be a mistake in the question or the options provided.