Question

How many kg of tea worth Rs 25 per kg must be blended with 30 kg 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. 32 kg
• B. 40 kg
• C. 36 kg
• D. 42 kg

Answer 1

The Correct Option is C

Price of cheaper tea = Rs 25 per kg
Price of costlier tea = Rs 30 per kg
Price of the mixture = Rs 30 per kg (after a 10% gain on the cost price)
Since there's a 10% gain, the cost price of the mixture is:
\(\text{Cost price of mixture} = \frac{30}{1.10} = 27.27 \, \text{Rs per kg}\)
\(\Rightarrow\;\)\(\text{Ratio of quantities} = \frac{\text{Cost of costlier} - \text{Cost of mixture}}{\text{Cost of mixture} - \text{Cost of cheaper}}\)
\(\Rightarrow\;\)\(\text{Ratio} = \frac{30 - 27.27}{27.27 - 25} = \frac{2.73}{2.27} = 1.2\)

Let the amount of cheaper tea be \(x\) kg. 
Since the ratio is 1.2, the amount of costlier tea is 30 kg:
\(\Rightarrow\;\frac{x}{30} = 1.2 \quad \Rightarrow \quad x = 1.2 \times 30 = 36 \, \text{kg}\)

Thus, 36 kg of tea worth Rs 25 per kg must be mixed with 30 kg of tea worth Rs 30 per kg.

The correct option is (C): 36 kg