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

To solve the problem of determining the ratio in which a grocer should mix two varieties of tea costing ₹60 per kg and ₹65 per kg in order to sell the mixture at ₹68.20 per kg with a profit of 10%, we must follow these steps: 

1. Calculate the Selling Price (SP) for 10% profit:
Given the selling price includes a 10% profit, the cost price (CP) of the mixture is calculated as follows:
\[ \text{SP} = \text{CP} + \text{Profit} \] \[ \text{Profit} = 10\% \text{ of CP} = 0.1 \times \text{CP} \] \[ \text{SP} = 1.1 \times \text{CP} \] Given: \(\text{SP} = ₹68.20\) 
\[ 68.20 = 1.1 \times \text{CP} \] \[ \text{CP} = \frac{68.20}{1.1} = ₹62 \]

2. Apply the Rule of Alligation to determine the ratio:
With Cost Prices (CP) of ₹60 and ₹65 per kg for the two varieties, and an average CP of the mixture being ₹62, set up the alligation:

\[ \begin{align*} \text{Cheaper variety} & : ₹60 \\ \text{Mean price of mixture} & : ₹62 \\ \text{Dearer variety} & : ₹65 \end{align*} \] \[ \begin{align*} \text{Cheaper - Mean} & = 62 - 60 = 2 \\ \text{Dearer - Mean} & = 65 - 62 = 3 \end{align*} \]

3. Find the ratio:
The ratio in which the varieties should be mixed is the inverse of the differences:

The ratio is \(3:2\).

Therefore, the grocer must mix the two varieties of tea in the ratio 3:2 to achieve a 10% profit by selling the mixture at ₹68.20 per kg.

Answer 2

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.