Question

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio

• A. 18 : 25
• B. 19 : 24
• C. 21 : 25
• D. 17 : 25

Answer 1

The Correct Option is B

Given:

• Selling price of the mixture = ₹40/kg
• Profit is 10% when tea A and tea B are mixed in the ratio 3:2
• Profit is 5% when mixed in the ratio 2:3

Let:

• \( a \): cost price per kg of tea A
• \( b \): cost price per kg of tea B

Step 1: Use the 10% profit case

Let the cost price of the mixture be \( x \). Given: \[ 1.1x = 40 \Rightarrow x = \frac{40}{1.1} \] In the 3:2 mixture, the cost price per kg is: \[ \frac{3a + 2b}{5} = \frac{40}{1.1} \Rightarrow 3a + 2b = \frac{200}{1.1} = 181.82\ldots \quad \text{(equation 1)} \] To avoid decimals, multiply both sides by 1.1: \[ 3.3a + 2.2b = 200 \quad \text{(1)} \]

Step 2: Use the 5% profit case

Similarly, for 5% profit: \[ 1.05x = 40 \Rightarrow x = \frac{40}{1.05} \] In the 2:3 mixture: \[ \frac{2a + 3b}{5} = \frac{40}{1.05} \Rightarrow 2a + 3b = \frac{200}{1.05} = 190.47\ldots \] Multiply both sides by 1.05: \[ 2.1a + 3.15b = 200 \quad \text{(2)} \]

Step 3: Subtract Equations (1) and (2)

From equations (1) and (2): \[ 3.3a + 2.2b = 200 \] \[ 2.1a + 3.15b = 200 \] Subtracting: \[ (3.3a - 2.1a) + (2.2b - 3.15b) = 0 \Rightarrow 1.2a = 0.95b \Rightarrow \frac{a}{b} = \frac{0.95}{1.2} = \frac{19}{24} \]

✅ Final Answer: The cost price ratio of tea A to tea B is 19:24