Question : Rice worth Rs.126 per kg and Rs.135 per kg are mixed with a third variety in the ratio of 1 : 1 : 2. If the mixture is worth Rs.153 per kg, then the price of the third variety per kg (in Rs.) is:
Option 1: 182.5
Option 2: 195.5
Option 3: 133.5
Option 4: 175.5
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Correct Answer: 175.5
Solution : The first and second varieties are mixed in equal proportions. Their average price = $\frac{126 + 135}{2}$ = Rs.130.50 So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at Rs.$x$ per kg, in the ratio 2 : 2 = 1 : 1. By the rule of allegation, we have, Ratio = (Higher value – Mean value) : (Mean value – Lower value) ⇒ $\frac{1}{1} = \frac{x – 153}{153 - 130.5}$ ⇒ $1 = \frac{x – 153}{22.5}$ ⇒ $x = 153 + 22.5$ $\therefore x = 175.5$ Hence, the correct answer is 175.5.
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Question : Wheat worth Rs. 80 per kg and Rs. 50 per kg is mixed with a third variety in the ratio $1:2:3$. If the mixture is worth Rs.75 per kg, then the price of the third variety per kg will be equal to:
Option 1: Rs. 95
Option 2: Rs. 85
Option 3: Rs. 80
Option 4: Rs. 90
Question : Rice worth INR 35 per kilogram and INR 38 per kilogram are mixed with a third variety in the ratio 2 : 1 : 2. If the mixture is worth INR 42 per kilogram, the price of the third variety per kilogram is:
Option 1: INR 52
Option 2: INR 53
Option 3: INR 54
Option 4: INR 51
Question : How many kilograms of rice costing Rs. 60 per kg must be mixed with 24 kg of rice costing Rs. 42 per kg so that there may be a gain of 12% by selling the mixture at Rs. 56 per kg?
Option 1: 22 kg
Option 2: 20 kg
Option 3: 19.2 kg
Option 4: 21.2 kg
Question : The price of a variety of a commodity is INR 7 per kg and that of another is INR 12 per kg. Find the ratio in which two varieties should be mixed so that the price of the mixture is INR 10 per kg.
Option 1: 3 : 4
Option 2: 2 : 3
Option 3: 4 : 5
Option 4: 2 : 5
Question : In what ratio should tea at Rs. 240 per kg be mixed with tea at Rs. 280 per kg so that, on selling the mixture at Rs. 324 per kg, there is a profit of 20%?
Option 1: 1 : 1
Option 2: 1 : 2
Option 3: 1 : 3
Option 4: 1 : 4
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