A mixture of sugar and water contains sugar and water in the ratio of

Question

A mixture of sugar and water contains sugar and water in the ratio of 3 : 2. Another mixture
of sugar and water contains sugar and water in the ratio 2 : 5. In what ratio should the two
mixtures be mixed so that the resulting mixture contains equal proportion of sugar and water?

A. 2 : 1
B. 3 : 1
C. 3 : 2
D. 4 : 1
E. None of these

amascarenhas · Accepted Answer

V1 - First mixture
V2 - Second mixture

Sugar = water in the final mixture
3/5V1+2/7V2=2/5V1+5/7V2
1/5V1=3/7V2
V1/V2= 15/7 which doesn't correspond to any of the solutions presented, so the answer must be E)

pushpitkc · Answer

Assume both the solutions to be 70 ml.

The mixture in ratio 3:2 -> 42:28 (sugar to water)
The mixture in ratio 2:5 -> 20:50 (sugar to water)

Since water and sugar must be in the same ratio in the resulting mixture the quantity of
sugar must be equal to quantity of sugar  42x + 20y = 28x + 50y  ->  14x = 30y

Therefore, the ratio in which the mixtures are to be added is  \frac{x}{y} = \frac{15}{7}  (Option E)

anair · Answer

I’ve used two methods to solve this, and I wanted to know why I am getting different answers. One method uses what has been shown above, which gives an answer of 15/7, and thus option E. The other is below.

2nd method:

The first mixture is in the ratio 3:2. Assuming 3kg of sugar in 2L of water. If you take 3 times that mixture, you get 9kg of sugar in 6L of water (the mixture ratio integrity is still maintained)

Adding that to the second mixture containing 2kg of sugar in 5L of water (mixture ratio of 2:5 maintained), we get a resulting solution that contains 9+2 =11kg of sugar in 6+5 =11L of water.

That is, equal portions of sugar and water. Therefore getting answer as B (3:1).

If this is wrong, I feel like i’m making a silly mistake somewhere because none of the ratio integrities are being broken.

Can anyone help?

Thanks!

Posted from my mobile device

manideep12 · Answer

Hey, can anyone say why below method is getting the wrong answer ??

I verified from options.

option B:- 3:1 which is 3 parts of mixture1 and 1 part of mixture2.

3(3:2) : 1(2:5) = mix1(9:6) : mix2(2:5) = 11 parts of sugar and 11 parts of water.

OA:- option E:- 4:1 which is 4 parts of mixture1 and 1 part of mixture2.

4(3:2) : 1(2:5) = mix1(12:8) : mix2(2:5) = 14 parts of sugar and 13 parts of water.

gota900 · Answer

... the resulting mixture the q of sguar must be equal to the q of water mate

gracie · Answer

let x and y=amounts of mixtures respectively
3x/5+2y/7=(x+y)/2
x/y=15/7
E

laurens123 · Answer

As usual: weighted averages formula:
 W1/W2=(C2-Avg)/(Avg-C1)

W1/W2=(3/5-1/2)/(1/2-2/7)=7/15 (Option E)

Arro44 · Answer

Could someone please share why B is not the correct answer?

Abir77 · Answer

Bunuel   VeritasKarishma  Please Help

KarishmaB · Answer

Abir77

When you say sugar:water = 3:2, you mean 3 parts of sugar for 2 parts of water. You cannot give different units to them.

Also, 3 parts + 2 parts means you have 5 parts of solution 1. If you take 3 times of this, you have 15 parts of solution 1. If each part is represented by 1 ml, you have 15 ml of solution 1.

In solution 2, you have 2 parts of sugar and 5 parts of water. So you have total 7 parts. If here also each part is equal to 1 ml, you have 7 ml of solution 2.

You are mixing these two to get 11 parts of sugar and 11 parts of water i.e. 22 parts of mixture or 22 ml of mixture. 
Solution 1 is 15 ml out of this and solution 2 is 7 ml out of this. 
Ratio = 15/7

Abir77 · Answer

Thanks a lot. Totally understood.

Basshead · Answer

We are told the first mixture is in the ratio 3:2. The second mixture is in the ratio 2.5 In what ratio should the two mixtures be mixed so that the resulting mixture contains equal proportion of sugar and water? We can use the weighted averages formula =

3/5 - 1/2 / 1/2 - 2/7
= 1/10 / 3/14
= 7 / 15

We need a ratio of 7:15, which isn't one of the answer choices. Answer is E.

3/5 - 1/2 / 1/2 - 2/7
= 1/10 / 3/14
= 7 / 15

We need a ratio of 7:15, which isn't one of the answer choices.  Answer is E.

vv65 · Answer

This question requires us to make many assumptions. An official question would be clearer.

These were are my assumptions:
 i. Any mixture of sugar and water is a sugar solution.

ii. 10 ml of water weighs 10 grams

iii. Mixture 1 has 3 grams of sugar for every 2grams/2ml of water. Similarly, mixture 2 has 2 grams of sugar for every 5grams/5ml of water. 
This is what 10 ml of each mixture will contain:
Mixture 1: 15gm sugar, 10gm water
Mixture 2: 4gm sugar, 10gm water

iv. The ratios in the answer choices refer to volumes not weights. 
So 2:1 means two parts by volume of mixture 1 and 1 part by volume of mixture 2.

The answer was still E. The question can be done by backsolving or by using algebra.

Posted from my mobile device

bumpbot · Answer

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A mixture of sugar and water contains sugar and water in the ratio of

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