Question

The ratio in which a grocer must mix two varieties of tea worth ₹60 per kg and ₹65 per kg so that by selling the mixture at ₹68.20 per kg, he may gain 10% is:

• A. 2 : 3
• B. 3 : 4
• C. 3 : 2
• D. 4 : 3

Answer 1

The Correct Option is C

The selling price (SP) is Rs. 68.20, and the cost price (CP) is calculated using the given profit percentage:

\(\text{Profit} = 10\% \implies SP = 1.1 \cdot CP\).

Substitute SP:

\(68.20 = 1.1 \cdot CP \implies CP = \frac{68.20}{1.1} = Rs. 62.\)

Using the rule of alligation, the ratio in which the two varieties must be mixed is given by:

\(\text{Ratio} = \frac{\text{Difference between higher price and mean price}}{\text{Difference between mean price and lower price}}.\)

Substitute values:

\(\text{Ratio} = \frac{65 - 62}{62 - 60} = \frac{3}{2}.\)

Thus, the grocer must mix the two varieties in the ratio 3 : 2.