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

This blend-and-profit question can also be solved with the alligation rule, once we convert the 10% profit condition into the cost price the blend should actually have.

1. Selling price of the blend is Rs. 30 per kg with a 10% gain, so the required average cost price per kg of the blend is $\dfrac{30}{1.10} = \dfrac{300}{11}$ Rs per kg.
2. By alligation, the ratio of the cheaper tea (Rs. 25) to the dearer tea (Rs. 30) equals (dearer price minus mean price) to (mean price minus cheaper price): $\left(30 - \dfrac{300}{11}\right) : \left(\dfrac{300}{11} - 25\right)$.
3. Simplify each part: $30 - \dfrac{300}{11} = \dfrac{330-300}{11} = \dfrac{30}{11}$, and $\dfrac{300}{11} - 25 = \dfrac{300-275}{11} = \dfrac{25}{11}$.
4. So the ratio of Rs. 25 tea to Rs. 30 tea is $\dfrac{30}{11} : \dfrac{25}{11} = 30:25 = 6:5$.
5. Since the given 30 kg of Rs. 30 tea corresponds to the "5" part of the ratio, each part is $30 \div 5 = 6$ kg. The Rs. 25 tea, being the "6" part, is $6 \times 6 = 36$ kg.

Alligation gives the mixing ratio directly from the three prices, so once that ratio is known, scaling it to match the known 30 kg quantity gives the answer quickly.

Let's summarize:

• 36 kg of the Rs. 25 per kg tea is required, matching option A.

This alligation route is often faster than setting up the full profit equation when only a ratio is needed.