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Emdad
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A 60 litre mixture of sugar and water contains sugar and 07 Oct 2021, 16:32
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65% (hard)

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58% (01:55) correct 42% (01:49) wrong based on 300 sessions

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A 60 litre mixture of sugar and water contains sugar and water in the ratio 2:3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1:1?
(A) 6
(B) 10
(C) 15
(D) 20
(E) None of these
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B
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chetan2u
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A 60 litre mixture of sugar and water contains sugar and Updated on: 05 Jan 2024, 04:41
Originally posted by chetan2u on 07 Oct 2021, 20:59.
Last edited by chetan2u on 05 Jan 2024, 04:41, edited 1 time in total.
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Emdad
A 60 litre mixture of sugar and water contains sugar and water in the ratio 2:3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1:1?
(A) 6
(B) 10
(C) 15
(D) 20
(E) None of these
Show more


1:1 means both should be 30 each.

But sugar is \(60*\frac{2}{5}=24\)

So, we have to increase the sugar by 6 kg.

When we replace one kg of mixture,
1) First we remove one kg of mixture: we remove 2/5 kg of sugar and 3/5 kg of water. and then add 1 kg to finally get 3/5 kg.
2) Then, we add one kg of sugar.
So, actual difference to sugar is: 1 kg added but 2/5 kg removed, so 1 - 2/5 or 3/5kg.

We have to increase sugar by 6kgs but each replacement of 1 kg gives us 3/5kg
So for 6 kgs => \(\frac{6}{\frac{3}{5}}=10\)
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Crytiocanalyst
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A 60 litre mixture of sugar and water contains sugar and 07 Oct 2021, 23:46
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Emdad
A 60 litre mixture of sugar and water contains sugar and water in the ratio 2:3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1:1?
(A) 6
(B) 10
(C) 15
(D) 20
(E) None of these
Show more

We have to make the mixture 1:1 or 30 kg each
in order to that we need to add 6 kg however we doing it by removing 2/5 of mixture and adding 1 kg to get 3/5

Therefore 6/(3/5) = 10
Therefore IMO B
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A 60 litre mixture of sugar and water contains sugar and 04 Jan 2024, 05:13
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Emdad
A 60 litre mixture of sugar and water contains sugar and water in the ratio 2:3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1:1?
(A) 6
(B) 10
(C) 15
(D) 20
(E) None of these
Show more

Solution:

  • We can also take the allegation approach to solve this question
  • The given solution has \(\frac{2}{2+3}=\) 40% of sugar whereas the replacing sugar will be 100% sugar
  • And the resulting solution we are looking for needs to have \(\frac{1}{1+1}=\) 50% of sugar
  • So, we can use allegation as follows
Attachment:
Screenshot 2024-01-04 173901.png
Screenshot 2024-01-04 173901.png [ 3.89 KiB | Viewed 9121 times ]

  • Assuming that we replace x ltrs of original solution with x ltrs of sugar, we can say \(\frac{60-x}{x}=50/10\)
    \(⇒\frac{60-x}{x}=5\)
    \(⇒60-x=5x\)
    \(⇒6x=60\)
    \(⇒x=10\)

Hence the right answer is Option B
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A 60 litre mixture of sugar and water contains sugar and 04 Jan 2024, 23:39
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Emdad
A 60 litre mixture of sugar and water contains sugar and water in the ratio 2:3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1:1?
(A) 6
(B) 10
(C) 15
(D) 20
(E) None of these
Show more

I find this logic simpler!

If I need 30 litres sugar and 30 litres water in the solution, I need to take out enough water to make it 30 litres.

Currently, it is 36 litres of water and 24 litres of sugar.
Each litre has 0.6 litres of water and 0.4 litres of sugar.

\(36-6=30\)
0.6*10=6

Therefore, I need to take out 0.6 litres 10 times (10 litres of 0.6 litres of water and 0.4 litres of sugar) to make it 30 litres of water!
Sugar removed = 0.4*10=4
Remaining sugar = 24-4 = 20

Now, if I add 10 litres of sugar, it will be 20+10=30 litres of sugar.

P.s. chetan2u, I don't get the logic of 3/5. How would the solution contain 3/5 sugar if 1 litre was taken out? Please if someone can explain!
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A 60 litre mixture of sugar and water contains sugar and 05 Jan 2024, 04:42
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Gprabhumir
Emdad
A 60 litre mixture of sugar and water contains sugar and water in the ratio 2:3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1:1?
(A) 6
(B) 10
(C) 15
(D) 20
(E) None of these

I find this logic simpler!

If I need 30 litres sugar and 30 litres water in the solution, I need to take out enough water to make it 30 litres.

Currently, it is 36 litres of water and 24 litres of sugar.
Each litre has 0.6 litres of water and 0.4 litres of sugar.

\(36-6=30\)
0.6*10=6

Therefore, I need to take out 0.6 litres 10 times (10 litres of 0.6 litres of water and 0.4 litres of sugar) to make it 30 litres of water!
Sugar removed = 0.4*10=4
Remaining sugar = 24-4 = 20

Now, if I add 10 litres of sugar, it will be 20+10=30 litres of sugar.

P.s. chetan2u, I don't get the logic of 3/5. How would the solution contain 3/5 sugar if 1 litre was taken out? Please if someone can explain!
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Hi,
I have just added some more details. Please let me know if you have a query still.
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A 60 litre mixture of sugar and water contains sugar and 17 Dec 2024, 09:55
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in the alligation method, shouldnt the ratio be 60:10 ?
SaquibHGMATWhiz
Emdad
A 60 litre mixture of sugar and water contains sugar and water in the ratio 2:3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1:1?
(A) 6
(B) 10
(C) 15
(D) 20
(E) None of these

Solution:

  • We can also take the allegation approach to solve this question
  • The given solution has \(\frac{2}{2+3}=\) 40% of sugar whereas the replacing sugar will be 100% sugar
  • And the resulting solution we are looking for needs to have \(\frac{1}{1+1}=\) 50% of sugar
  • So, we can use allegation as follows
Attachment:
Screenshot 2024-01-04 173901.png

  • Assuming that we replace x ltrs of original solution with x ltrs of sugar, we can say \(\frac{60-x}{x}=50/10\)
    \(⇒\frac{60-x}{x}=5\)
    \(⇒60-x=5x\)
    \(⇒6x=60\)
    \(⇒x=10\)

Hence the right answer is Option B
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A 60 litre mixture of sugar and water contains sugar and 03 Jan 2025, 19:23
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KarishmaB chetan2u GMATinsight

Since mixture should be replaced by sugar ,
lets solve from the water perspective.

Final conc of water =50%
Initial conc of water = 60%
Let = x literes of the mixture should be replaced by sugar


50 = 60 ((60 - x )/ 60 )
x=10 litres of the mixture should be replaced by sugar (Answer B).
Emdad
A 60 litre mixture of sugar and water contains sugar and water in the ratio 2:3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1:1?
(A) 6
(B) 10
(C) 15
(D) 20
(E) None of these
Show more
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