Problem Solving

Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?

A. 1:10
B. 1:5
C. 2:7
D. 3:8
E. 5:7

Can someone explain the best approach to solve these kind of problems?

Thanks.

I assumed that it was mixed in ratio a:b and then worked out given information to get answer as

B) 1:5

Is there a shorter method?

vatish wrote:I assumed that it was mixed in ratio a:b and then worked out given information to get answer as

B) 1:5

Is there a shorter method?

Could you please elaborate?

If selling the mixture at 7 cents per ounce makes a profit of 20 percent, we can set up the following equation:

1.2x = 7 (I would convert to a fraction to make solving for x easier)

6x/5 = 7

6x = 35

x = 35/6 = 5 5/6 (or 5.833... if you solved for a decimal)

If we know the price of the varieties being mixed, then the weighted average is determined by the ratio of the two varieties. 5.833 is about .83 away from 5 and about .17 away from 6. .17/.83 = ~1:5

If we think about it visually:


5-------5.5---5.83-6

We can see that, for the average to be closer to 6, we must have more of the 6-cent variety. The proportion is given by the distance from the average to the two ends of the number line. 6 - 5.83 = .17 and 5.83 - 5 = .83. .17:.83 = ~1:5.

PGMAT wrote:Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?

A. 1:10
B. 1:5
C. 2:7
D. 3:8
E. 5:7

Can someone explain the best approach to solve these kind of problems?

Thanks.

We can plug in the answers, which represent the ratio of 5-cent rice to 6-cent rice.

Answer choice C: 2:7
Total cost of 2 ounces of 5-cent rice and 7 ounces of 6-cent rice = 2*5 + 7*6 = 52.
Revenue from 9 ounces of rice with a selling price of 7 cents per ounce = 9*7 = 63.
Percent profit = (63-52)/52 * 100 = 21.1%.
Too much profit.
Eliminate C.

To decrease the profit, the cost must include a greater proportion of 6-cent rice, the more expensive rice.

Answer choice B: 1:5
Total cost of 1 ounce of 5-cent rice and 5 ounces of 6-cent rice = 1*5 + 5*6 = 35.
Revenue from 6 ounces of rice with a selling price of 7 cents per ounce = 6*7 = 42.
Percent profit = (42-35)/35 * 100 = 20%.
Success!

The correct answer is B.

thanks, i'm using GMATGuruNY method but cost me 2-3min to solve this problem

Dear Mitch
I think Using Allegation will be more easy and faster than plugging in the answer options.
Considering "Cost" as the common factor, below will be the allegation chart.
Variety 1 Variety 2
Cost =5 Cost =6
Mixture
Cost =7/1.2

(6-7/1.2) (7/1.2-5)
=1/6 =5/6
Answer is 1:5

krishna239455 wrote:Dear Mitch
I think Using Allegation will be more easy and faster than plugging in the answer options.
Considering "Cost" as the common factor, below will be the allegation chart.
Variety 1 Variety 2
Cost =5 Cost =6
Mixture
Cost =7/1.2

(6-7/1.2) (7/1.2-5)
=1/6 =5/6
Answer is 1:5

hey krishna didnt get yr highlighted step..
can u pls explain

krishna239455 wrote:Dear Mitch
I think Using Allegation will be more easy and faster than plugging in the answer options.
Considering "Cost" as the common factor, below will be the allegation chart.
Variety 1 Variety 2
Cost =5 Cost =6
Mixture
Cost =7/1.2

(6-7/1.2) (7/1.2-5)
=1/6 =5/6
Answer is 1:5

Yup, that's pretty much my approach to questions like this.

Hi All,

Simple way would be to take the variables, consider this method.

x be the amount of rice bought for 5 cents.
y be the amount of rice bought for 6 cents.
So total amount of rice is x+y

Total cost price = 5x+6y
Total sell price = 7(x+y)

profit is 20%, so
7(x+y)/5x+6y = 120/100 = 1.2
7x+7y = 6x+7.2y
x=0.2y
5x=y
x/y= 1/5