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
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Correct Answer: INR 51
Solution : Given ratio = 2 : 1 : 2 Let the price of the third variety be INR $x$. Let us take 2 kg, 1 kg, and 2 kg of rice worth INR 35 per kg, INR 38 per kg, and INR $x$ per kg, respectively. Total worth of (2 kg + 1 kg + 2kg) = 5 kg of mixture is 35 $\times$ 2 + 38$ \times$ 1 + $x \times$ 2 = 70 + 38 + 2$x$ = 108 + 2$x$ .....(1) According to the question, 1 kg of mixture = INR 42 Worth of 5 kg of mixture = (42 × 5) = INR 210.......(2) $\therefore$ from equations (1) and (2), 108 + 2$x$ = 210 ⇒ 2$x$ = 102 $\therefore$ $x$ = INR 51 Hence, the correct answer is INR 51.
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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
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 : 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 : The price of rice is decreased by 25% and therefore a person can purchase 30 kg more rice in the same expenditure. If the expenditure is INR 5,400, then what was the original price of rice per kg?
Option 1: INR 90 per kg
Option 2: INR 60 per kg
Option 3: INR 75 per kg
Option 4: INR 50 per kg
Question : In a mixture of three varieties of tea, the ratio of their weights is 4 : 5 : 8. If 5 kg tea of the first variety, 10 kg tea of the second variety and some quantity of tea of the third variety are added to the mixture, the ratio of the weights of three varieties of tea becomes 5 : 7 : 9. In the final mixture, the quantity (in kg) of the third variety of tea was:
Option 1: 42
Option 2: 45
Option 3: 48
Option 4: 40
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