Question

How many kgs of tea worth Rs. 25 per kg must be blended with 30 kgs of tea worth Rs. 30 per kg so that by selling the blended variety at Rs. 30 per kg there should be a gain of 10%?

• A. 36 kgs
• B. 40 kgs
• C. 32 kgs
• D. 42 kgs

Hint:

Convert the 10% profit condition into the required average cost price of the blend, then use alligation on the three prices.

Answer 1

The Correct Option is A

Step 1: Set up the cost of the blend.
Let the quantity of Rs. 25 tea be \(x\) kg. The total cost price of the blend is \(25x + 30 \times 30 = 25x + 900\) for a total weight of \((x+30)\) kg.

Step 2: Use the selling price and profit percentage to find the required cost price.
The blend is sold at Rs. 30 per kg for all \((x+30)\) kg, so total selling price \(= 30(x+30)\). Since there is a 10% gain, selling price equals cost price times \(\dfrac{110}{100}\), so \[ (25x+900) \times \dfrac{110}{100} = 30(x+30) \]

Step 3: Solve the equation for x.
Multiply out: \(\dfrac{110}{100}(25x+900) = 27.5x + 990\), and the right side is \(30x + 900\). So \(27.5x + 990 = 30x + 900\), which gives \(990 - 900 = 30x - 27.5x\), so \(90 = 2.5x\), and \(x = 36\).

Final Answer:
36 kg of the Rs. 25 tea must be blended in. \[ \boxed{36 \text{ kg}} \]