In what proportion must rice at $3.10 per kg be mixed with rice at $3.

Question

In what proportion must rice at $3.10 per kg be mixed with rice at $3.60 per kg so that the mixture be worth $3.25 per kg?

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

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.

Therefore  \frac{Q_1}{Q_2} = \frac{3.6 - 3.25}{3.25 - 3.1}

\frac{Q_1}{Q_2} = \frac{0.35}{0.15} = \frac{7}{3}

\frac{Q_1}{Q_2} = \frac{P_2 - P}{P - P_1}

Option D

Arun Kumar

Abhishek009 · Answer

310 ___________________________ 360

___________ 325 ___________

35 ___________________________ 15

Or,  7:3 , Answer must be (D)

abhinavsodha800 · Answer

HI Abhishek, can u explain the approach u are using to solve this question ?

Fullridedreams · Answer

How do you know which one to put on top in the ratio? This is a hurdle I am facing in word problems like these alot.

e3thekid · Answer

You can assign a varible to the weight of rice at $3.10 per kg (x) and assign a variable to the weight of rice at $3.60 per kg (y)

This question is asking for the proportion of rice weighed at $3.10 per kg to rice weighed at $3.60 per kg. -> x/y

You can set this up as a weighted average problem. We are told that the overall mixture will be worth $3.25 per kg.

Setting up the equation as:
3.10x + 3.60y / x + y = 3.25
3.10x + 3.60y = 3.25x + 3.25y (Multiply the entire equation by 100 to get rid of the decimals if it is easier for you.

310x +360y = 325x + 325y
35y = 15x (simplify by dividing both sides by 5)
7y = 3x (rearrange the varibles to x/y to get final proportion)

7/3 = x/y

A proportion or ratio can be written as x/y or x:y so we get  7:3  as final proportion.

Option D

daynesj24 · Answer

How did you get 35 and 15 in the bottom part?

Thanks

In what proportion must rice at $3.10 per kg be mixed with rice at $3.

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 proportion must rice at $3.10 per kg be mixed with rice at $3.

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