Cereal A is 10% sugar by weight, whereas healthier but less delicious

Question

Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?

(A) 2:9
(B) 2:7
(C) 1:6
(D) 1:4
(E) 1:3

I took this question from MGMAT. However, I'm not satisfied with the approach and explanation and wish there was an easy way to solve this. Can someone please help explain?

Thanks!

Spidy001 · Accepted Answer

(10/100)A+(2/100)B = (4/100)(A+B)
6A =2B
=> A/B = 1/3

Answer is E.

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MHIKER · Answer

The proportion needed of each starting percentage is the positive difference between the other two percentages.

Wt (10%) = 4-2 = 2

Wt( 2%) = 10-4= 6 
cereal A to B = 2/6 = 1/3

fluke · Answer

Please read this: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... -averages/

subhashghosh · Answer

Using Alligation :

Ratio of A / Ratio of B = (Avergate Wt of Mixture - Wt of B)/(Wt of A - Avergate Wt of Mixture)

=> Ratio of A / Ratio of B = (4 - 2)/(10 - 4) = 2/6 = 1/3

So they should be mixed in the ratio 1:3

Answer - E

mniyer · Answer

Excellent. Thank you mate. I liked the scale method lot better

10%------------|--------4%------2% Distance between 10 and 4 is 6 Distance between 4 and 2 is 2. Flip the numbers while forming the ratio. So 2:6 which is 1:3. Phew!

adityadon · Answer

for such questions , just write down figures in following way on paper 
10 2
 4
2 6 which is 1:3

What i did here is 10-4= 6 and 4-2 = 2 
line number 3 is your answer. 
Hope this helps !!!

Regards
aditya_don

EMPOWERgmatRichC · Answer

Hi All,

This is an example of a "Weighted Average" question. These types of prompts can be solved in a variety of ways - here's how you can use the Weighted Average Formula to answer the question:

We're told that two types of cereal....
1) A certain amount of Cereal A, which is 10% sugar by weight
2) A certain amount of Cereal B, which is 2% sugar by weight

....are mixed together to form a Cereal that is 4% sugar by weight.

We're asked for the ratio of Cereal A to Cereal B in the new cereal.

A = # of ounces of Cereal A
B = # of ounces of Cereal B

/(A+B) = .04

.1A + .02B = .04A + .04B
.06A = .02B

6A = 2B

Since the question asks for A/B, we just have to do a little more math....

A/B = 2/6 = 1/3

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

stonecold · Answer

Hey @cheetan2u 
i did it exactly as  EMPOWERgmatRichC  quoted.
Each and every step.
And got the answer too.
Any quicker ways?
Can we solve it any other way as the people above are quoting=> "Weighted average"
I can you explain this terminology.

Any theory would be helpful.

MarkusKarl · Answer

Simply set up an equation and solve for the answer.

Weights:
x+y=1
y=1-x
1=(1-x)+x

Solution equation with weights(note that x = part of cereal A/whole solution):
4=10x+2(1-x)
2=8x
1/4=x

As 1/4 of the solution is cereal A, the rest (3/4) must be cereal B.

1:3 is thus the answer.

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Cereal A is 10% sugar by weight, whereas healthier but less delicious

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Cereal A is 10% sugar by weight, whereas healthier but less delicious

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