In what ratio should two varieties of tea at Rs. 60 per kg and Rs.120 per kg be mixed together so that by selling the mixture at Rs.96 per kg, a profit of Rs.20% is obtained?

Step 1: Find the cost price of the mixture

• Let the cost price of the mixture be x
• Selling price = Rs.96
• Profit = 20%

x + 20% of x = 96
⇒ x × (1 + 20/100) = 96
⇒ x × 1.2 = 96
⇒ x = 96 / 1.2 = Rs.80

Step 2: Apply alligation rule

First tea (Rs.60)          Second tea (Rs.120)
       \                         /
        \                       /
        Cost price = Rs.80
        /                       \
       /                         \
   120 - 80 = 40           80 - 60 = 20

Required ratio = 40 : 20 = 2 : 1

Answer: 2 : 1

The two varieties of tea should be mixed in the ratio 2:1 (Rs.60/kg : Rs.120/kg) to make a 20% profit when selling at Rs.96/kg.

This is a classic alligation problem where understanding profit and cost dynamics is crucial. By calculating the adjusted cost price first, we ensure that the mixture yields the desired profit. Such problems are commonly found in business math and aptitude sections of competitive exams.