In what ratio must rice at $9.30 per Kg be mixed with rice at $10.80

Solution:

Notice that $10, the average cost, is slightly closer to $9.30 than it’s to $10.80. Furthermore, $9.30 is 70 cents less than $10 whereas $10.80 is 80 cents more than $10; therefore, we need eight kg of $9.30 rice to “balance” with seven kg of $10.80 rice to obtain an average of $10.

Alternate Solution:

Let’s determine x, the number of kg of rice costing $10.8 per kg, that should be mixed with 1 kg of rice costing $9.3 per kg such that the resulting mixture costs $10 per kg

. Since we are mixing x kg of the more expensive rice with 1 kg of the less expensive rice, we can write the following equation:

(1 * 9.3 + x * 10.8) / (1 + x) = 10

9.3 + (10.8)x = 10 + 10x

(0.8)x = 0.7

x = 0.7/0.8 = 7/8

This tells us that 1 kg of rice costing $9.3 per kg, when combined with 7/8 kg of rice costing $10.8 per kg, produces a mixture which costs $10 per kg. Thus, the ratio of the two kinds of rice is 1/(7/8) = 8/7, for the mixture costing $10 per kg. The answer is 8/7, or 8 : 7.

Answer: C

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For questions like these involving the weighted average : Q1 / Q2 = P2 - P / P - P1, how do I know what Q1 is vs Q2 is? There's no clear indicator and I got mixed up so I ended up with B instead.

Hi. in such cases you normally assign the cheaper priced goods as Q1 and the costlier goods as Q2. get the required ratio and then see if the question is asking for Q1/Q2 or Q2/Q1. I normally use this and have found it to be helpful.

Arun Kumar

Response:

The question is asking for the ratio of the $9.30 rice to the $10.80 rice in the mixture. If you decide to use the Q1 / Q2 formula, Q1 must represent the $9.30 rice and Q2 must represent the $10.80 rice.

Option B is actually the ratio of the $10.80 rice to the $9.30 rice. You could have figured out that B can’t be correct by noticing that if we were to mix equal amounts of the two kinds of rice, the mixture we obtain would have cost (9.30 + 10.80)/2 = $10.05, which is greater than $10. That’s why the amount of $9.30 rice in the mixture should be greater than the amount of $10.80 rice. If you were able to determine that the ratio of the two kinds of rice was 7 : 8 but you were not sure whether the answer should be B or C, you could have used this reasoning to conclude that the answer should be C.