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

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Intern
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A mixture of sugar and water contains sugar and water in the ratio of  [#permalink]

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New post 28 Nov 2018, 08:12
1
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A
B
C
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E

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Question Stats:

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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
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Re: A mixture of sugar and water contains sugar and water in the ratio of  [#permalink]

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New post 28 Nov 2018, 08:42
2
1
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)
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A mixture of sugar and water contains sugar and water in the ratio of  [#permalink]

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New post 28 Nov 2018, 10:29
1
bryton wrote:
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


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)
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Re: A mixture of sugar and water contains sugar and water in the ratio of  [#permalink]

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New post 04 Dec 2018, 00:41
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!

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A mixture of sugar and water contains sugar and water in the ratio of  [#permalink]

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New post 05 Dec 2018, 19:33
1
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.
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Re: A mixture of sugar and water contains sugar and water in the ratio of  [#permalink]

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New post 18 Dec 2018, 02:44
pushpitkc wrote:
bryton wrote:
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


Assume both the solutions to be 70 ml.

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

... the resulting mixture the q of sguar must be equal to the q of water mate
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A mixture of sugar and water contains sugar and water in the ratio of  [#permalink]

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New post 18 Dec 2018, 11:53
bryton wrote:
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


let x and y=amounts of mixtures respectively
3x/5+2y/7=(x+y)/2
x/y=15/7
E
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Re: A mixture of sugar and water contains sugar and water in the ratio of  [#permalink]

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New post 13 Feb 2019, 05:02
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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)
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Re: A mixture of sugar and water contains sugar and water in the ratio of  [#permalink]

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New post 13 Feb 2019, 05:27
Could someone please share why B is not the correct answer?
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Re: A mixture of sugar and water contains sugar and water in the ratio of   [#permalink] 13 Feb 2019, 05:27
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