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

Question

In what ratio must rice at $9.30 per Kg be mixed with rice at $10.80 per Kg so that the mixture be worth $10 per Kg?

A. 3:7
B. 7:8
C. 8:7
D. 6:5
E. 6:1

CrackverbalGMAT · Answer

By the rule of alligations,  \frac{Q_1}{Q_2} = \frac{P_2 - P}{P - P-1}

Where Q1 and Q2 are the quantities of the cheaper and costlier rice

P1 and P2 are their Prices and P is the average price.

\frac{Q_1}{Q_2} = \frac{10.8 - 10}{10 - 9.30} = \frac{0.8}{0.7} = \frac{8}{7}

Option C

Arun Kumar

kmempire · Answer

Since the cheaper kind was presented first, surely it's 7:8 therefore B?

ScottTargetTestPrep · Answer

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

CEdward · Answer

CrackVerbalGMAT   ScottTargetTestPrep

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.

CrackverbalGMAT · Answer

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

ScottTargetTestPrep · Answer

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.

mlc1997 · Answer

i did the following:

9.30 -------------10 -------------10.80

9.30 is .7 away from 10, 10.80 is .8 away from 10 
therefore, the closer number holds more weight. you flip the distances 
9.30 holds .8 of weight and 10.80 holds .7 of weight so .8:.7, multiply by 10 to eliminate decimals and you get 8:7

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards