what about salt and pepper?

To summarize: the dressing contains 5/8 olive oil, 2/8 vinegar, and the remaining 1/8 is and even mixture of salt, pepper and sugar.

If we rewrite the fractions with a denominator 24, we get the following:
The correct dressing contains 15/24 olive oil, 6/24 vinegar, and the remaining 3/24 is and even mixture of salt, pepper and sugar.

In other words:
The dressing contains 15/24 olive oil, 6/24 vinegar, 1/24 salt, 1/24 pepper and 1/24 sugar.

So for example, one correct mixture could have the following:
15 cups of olive oil, 6 cups of vinegar, 1 cup of salt, 1 cup of pepper and 1 cup of sugar.

So, if Miguel doubles the vinegar and forgets to sugar all together, then the above combination of ingredients becomes:
15 cups of olive oil, 12 cups of vinegar, 1 cup of salt, and 1 cup of pepper.

So we have a total of 29 cups of ingredients, and 15 cups are olive oil.
So, 15/29 of the botched dressing is olive oil

Answer: A

KarunMendiratta,
Sir,

Can you please explain how can the summation of the mixture's contents be greater than 1? I'm a little confused because I was thinking that 2(Vinegar) + Olive oil + salt + pepper should equal 1.

If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion ......

The contents of new mixture will not be same as of the original mixture!
The summation would have been one, when we double the vinegar and compensated it with other ingredients.

For example, in 24 cups - 15 cups are olive oil, 6 cups are vinegar, and 1 cup each of salt, pepper and sugar.
Now when you take 12 cups of vinegar, 15 cups of olive oil and 1 cup each of salt and pepper, you will have 29 cups instead of 24 cups.

Got it, sir. Thanks!

Let Y be total original mixture and A for each amount of salt, pepper and sugar.
5Y/8 + Y/4 + 3A = Y
Y = 24A

If vinegar was doubled and sugar removed from mixture we have
Y/4-A = 5A
Which means 5A was added to original mixture which makes the botched mixture 29A.
If botched mixture = 12A + 2A, then new amount of olive oil = 15A
That gives the fraction to be 15/29.

Solution in Parts -

Olive = 5/8
Vinegar = 1/4

Total = 7/8.
Remaining=1/8

Salt, Pepper, Sugar = (1/8)/3 = 1/24 each

Now consider the parts;
Olive = 5/8 = 15/24
Vinegar = 1/4 = 6/24
Salt=1/24
Sugar=1/24
Pepper=1/24

For 24 parts mixture; 15 part olive; 6 vinegar; 1 salt; 1 pepper; 1 sugar

Double the vinegar - 6*2=12 parts
Leave the sugar = 1-1=0

New mixture would be;
15 parts olive; 12 parts vinegar; 1 salt; 1 pepper

Total: 15+12+1+1=29 parts
Olive= 15 parts

Ratio (Olive/Mixture) = 15/29

Answer Choice: "A"

why did you add olive oil we had to find that?

Olive oil \(=\frac{5}{8} = \frac{15}{24}\) --> 15 parts out of 24;

Vinegar \(= \frac{1}{4} = \frac{6}{24}\) --> 6 parts out of 24;

Salt + pepper + sugar \(= 1-(\frac{15}{24}+\frac{6}{24})= \frac{3}{24}\), so each \(= \frac{1}{24}\) --> 1 part out of 24 each.

If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are olive oil --> proportion \(= \frac{15}{29}\).

Answer: A.

Easy way to do this problem is to assume the total to be 240 coz it's easily divisible by the fractions given.
(We have to figure out which is the easier value to play with... considering it to be 100 would have made the solution harder to achieve but would have provided the same answer... so 240 it is!!)
Then for Olive: 5/8*240=150
for Vinegar: 1/4*240=60
now mix of salt, pepper and sugar : 240-(150+60) = 30 ie(10-10-10 for salt, pepper and sugar each)

Our bruh f***ed things up.
Vinegar new= 2*60=120 and forgot sugar so we won't add 10 in the total

Total= 150+120+20(this is only of salt and pepper)
=290
now olive oil/total =150/290 = 15/29

so answer A. Hope it helps!!

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