Answer :
Mixed fruit juice is sold by mixing two kinds of juices. one of Rs 110 per kg and another of Rs 124 per kg such that after selling it at Rs. 150 per kg there is a gain of 25%. So, the two juices should be mixed in a ratio 2.5:1.
The first step in solving this problem is determining the cost price per kilogram once the gain of 25% is considered.
To achieve this, we find 25% of the selling price, which is Rs. 150 per kg. The formula we use to calculate the cost price is selling price * (100 / (100 + gain percent)). In this case, the cost price is going to be Rs. 150 * (100 / (100 + 25)), which results to Rs. 120.
Once we have the cost price, we use the method of allegation to solve for the ratio in which the juices should be mixed. The method of allegation involves finding the difference between the cost price and each of the costs of the two juices.
We subtract the cost of the first juice from the cost price to get Rs. 120 - Rs. 110 = Rs. 10.
We subtract the cost price from the cost of the second juice to get Rs. 124 - Rs. 120 = Rs. 4.
Hence, the required ratio in which the juices should be mixed is 10:4.
To make it simpler, we can express it as a fraction and simplify further. Hence, the required ratio becomes 10/4 = 2.5.
Therefore, the two juices should be mixed in the ratio 2.5:1.
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