The cost of type 1 rice is Rs. 15 per kg and type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3 then find the price per kg of the mixed variety of rice. A. 18 B. 16 C. 14 D. 12
ANSWER
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Hint: We have to find the amount and price of each type of rice(one kg) of the mixed variety and then we can easily find the price of one kg of mixed variety by adding the price for both types of rice.
Complete step-by-step answer: As we know that 1 kg = 1000 grams As we know that the Type 1 and Type 2 are mixed in a ratio of 2 : 3 to form a mixed variety of rice. Let the amount of rice of type 1 in one kg of mixed variety of rice will be 2x grams. So, the amount of rice of Type 2 in one kg of mixed variety of rice will be 3x grams. Now as we know that both types of rice when added then the amount of mixed variety of rice is 1 kg or 1000 grams. So, 2x + 3x = 1000 5x = 1000 Dividing both sides of the above equation by 5. We get, x = 200 grams So, 1 kg of mixed variety of rice will have 2x = 400 grams of rice of type 1. And, 1 kg of mixed variety of rice will have 3x = 600 grams of rice of type 2. Now the price of 1 kg or 1000 grams of rice of type 1 is Rs. 15. So, the price for 1 grams of the rice of type 1 will be equal to Rs. \[\dfrac{{15}}{{1000}}\] Then the price for 400 grams of rice of type 1 will be equal to Rs. \[400 \times \dfrac{{15}}{{1000}}\] = Rs. 6 And the price of 1 Kg or 1000 grams of rice of type 2 is Rs. 20. So, the price for 1 grams of the rice of type 2 will be equal to Rs. \[\dfrac{{20}}{{1000}}\] Then the price for 600 grams of rice of type 2 will be equal to Rs. \[600 \times \dfrac{{20}}{{1000}}\] = Rs. 12 Now as we know that the 1 kg of rice of mixed variety has 400 grams of rice of type 1 and 600 grams of rice of type 2. So, the price for 1 kg of rice of mixed variety will be equal to the sum of the price of 400 grams of rice of type 1 and 600 grams of rice of type 2. So, the price of 1 kg of rice of mixed variety will be equal to Rs. 6 + Rs. 12 = Rs 18. Hence, the correct option will be A.
Note: Whenever we come up with this type of problem then first we had to find the amount of rice of each type in the 1 kg of mixed variety of rice and after that we had to find the price of amount of rice of each type used in 1 kg of mixed variety and then add them to get the required price of 1 kg of rice of mixed variety. And we should remember that if x things cost Rs. y. Then one thing of same type will cost Rs. \[\dfrac{y}{x}\]