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Mugdho
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2/5 th of mixture of milk and water is replaced by orange juice and Updated on: 13 Jun 2024, 07:46
Originally posted by Mugdho on 05 Feb 2021, 08:48.
Last edited by Bunuel on 13 Jun 2024, 07:46, edited 2 times in total.
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2/5 th of mixture of milk and water is replaced by orange juice and the ratio of Milk, Water and Orange juice in the resulting mixture becomes 4:5:6 respectively. Initial quantity of milk in the mixture is 20 litres less than that of water. Then What % of resulting mixture should be taken out, due to which total quantity of milk and orange juice in the final mixture becomes 66 litres ?

A. 35%
B. 55%
C. 45%
D. 72%
E. 64%
 
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2/5 th of mixture of milk and water is replaced by orange juice and 05 Feb 2021, 10:34
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Mugdho
2/5 th of mixture of milk and water is replaced by orange juice and the ratio of Milk, Water and Orange juice in the resulting mixture becomes 4:5:6 respectively. Initial quantity of milk in the mixture is 20 litres less than that of water. Then What % of resulting mixture should be taken out, due to which total quantity of milk and orange juice in the final mixture becomes 66 litres ?

A)35%
B)55%
C)45%
D)72%
E)64%

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So M:W:O = 4:5:6 =4x:5x:6x
Now initial mixture is less by 2/5, so 3/5 of M=4x.....\(M_i=\frac{20x}{3}\)
Similarly \(W_i=\frac{25x}{3}\)

Given that \(W_i-M_i=20=\frac{25x}{3}-\frac{20x}{3}.........\frac{5x}{3}=20.......x=12\)

Thus M, W and O are 4*12, 5*12 and 6*12 respectively.
Total M and O is 48+72=120, but we want this to be just 66 litres.
So we have to take out 120-66 or 54 from the resulting mixture.
% to be taken out = \(\frac{54}{120}*100=9*5=45%\)

C
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2/5 th of mixture of milk and water is replaced by orange juice and 13 Jun 2024, 07:42
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Mugdho
2/5 th of mixture of milk and water is replaced by orange juice and the ratio of Milk, Water and Orange juice in the resulting mixture becomes 4:5:6 respectively. Initial quantity of milk in the mixture is 20 litres less than that of water. Then What % of resulting mixture should be taken out, due to which total quantity of milk and orange juice in the final mixture becomes 66 litres ?

A)35%
B)55%
C)45%
D)72%
E)64%

Posted from my mobile device
So M:W:O = 4:5:6 =4x:5x:6x
Now initial mixture is less by 2/5, so 3/5 of M=4x.....\(M_i=\frac{20x}{3}\)
Similarly \(W_i=\frac{25x}{3}\)

Given that \(W_i-M_i=20=\frac{25x}{3}-\frac{20x}{3}.........\frac{5x}{3}=20.......x=12\)

Thus M, W and O are 4*12, 5*12 and 6*12 respectively.
Total M and O is 48+72=120, but we want this to be just 66 litres.
So we have to take out 120-66 or 54 from the resulting mixture.
% to be taken out = \(\frac{54}{120}*100=9*5=45%\)

C
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chetan2u

­I am confused how you are getting 25x/3 and 20x/3­
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2/5 th of mixture of milk and water is replaced by orange juice and 13 Jun 2024, 09:37
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2/5 th of mixture of milk and water is replaced by orange juice and the ratio of Milk, Water and Orange juice in the resulting mixture becomes 4:5:6 respectively. Initial quantity of milk in the mixture is 20 litres less than that of water. Then What % of resulting mixture should be taken out, due to which total quantity of milk and orange juice in the final mixture becomes 66 litres ?

So, we have 4x, 5x and 6x of Milk, Water and Orange in the resulting mixture.
Let M and W be the quantity in the original/initial mixture W+M, so after 2/5th is taken out, we are left with 3/5(W+M) or 3M/5 and 3W/5 in the resulting mixture. But we know that the resulting mixture has 4x milk, so 3M/5 = 4x or M = 4x*5/3 = 20x/3.
Similarly, 3W/5 = 5x or W=5x*5/3 = 25x/3.

pakman95, hope it helps
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2/5 th of mixture of milk and water is replaced by orange juice and 13 Jun 2024, 09:46
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Mugdho
2/5 th of mixture of milk and water is replaced by orange juice and the ratio of Milk, Water and Orange juice in the resulting mixture becomes 4:5:6 respectively. Initial quantity of milk in the mixture is 20 litres less than that of water. Then What % of resulting mixture should be taken out, due to which total quantity of milk and orange juice in the final mixture becomes 66 litres ?
 
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­Another way to look at it..

Intial: M and W differ by 20, that is W-M = 20.
Resulting mix: We have 3/5 of M and 3/5 of W left when 2/5 is taken out....If W-M = 20, then 3/5 of W - 3/5 of M = 3W/5 - 3M/5 = 3/5(W-M) = 3/5 * 20 = 12.
Thus, if quantity is 4x, 5x and 6x, then 4x-3x = 12 or x=12.

So, the quantity of M, W and O is 48, 60 and 72 respectively.

Next we cannot reduce ONLY milk and orange, it will be all three, but since we talk of final quantity of only these two, let us concentrate on these two.
Actual quantity = 48+72 or 120, so we have to reduce 120 to 66. As a % reduction = (120-66)/120 * 100 = 45%
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2/5 th of mixture of milk and water is replaced by orange juice and 10 Sep 2024, 08:27
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Mugdho
2/5 th of mixture of milk and water is replaced by orange juice and the ratio of Milk, Water and Orange juice in the resulting mixture becomes 4:5:6 respectively. Initial quantity of milk in the mixture is 20 litres less than that of water. Then What % of resulting mixture should be taken out, due to which total quantity of milk and orange juice in the final mixture becomes 66 litres ?

A. 35%
B. 55%
C. 45%
D. 72%
E. 64%

Show more
­Just wanted to add that if all terms in a ratio are multiplied or divided by the same number the ratio will remain the same.

Since M:W:O --> 4:5:6 and M and W as a quantity was reduced to 3/5, then the initial ratio of M:W will also be 4:5

Now that you know 4x = 5x - 20, x = 20
So, initial mixture would be 180, M:W --> 80:100
Now the current mixture would then M:W:O be 3/5*80: 3/5*100: 2/5*180

M+O =120, Now we have to bring this quantity down to 66, 120-66 = 54
therefore, 54/120 = 45%

C is the answer.
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2/5 th of mixture of milk and water is replaced by orange juice and 17 Sep 2024, 03:34
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Ankur17000
Mugdho
2/5 th of mixture of milk and water is replaced by orange juice and the ratio of Milk, Water and Orange juice in the resulting mixture becomes 4:5:6 respectively. Initial quantity of milk in the mixture is 20 litres less than that of water. Then What % of resulting mixture should be taken out, due to which total quantity of milk and orange juice in the final mixture becomes 66 litres ?

A. 35%
B. 55%
C. 45%
D. 72%
E. 64%

­Just wanted to add that if all terms in a ratio are multiplied or divided by the same number the ratio will remain the same.

Since M:W:O --> 4:5:6 and M and W as a quantity was reduced to 3/5, then the initial ratio of M:W will also be 4:5

Now that you know 4x = 5x - 20, x = 20
So, initial mixture would be 180, M:W --> 80:100
Now the current mixture would then M:W:O be 3/5*80: 3/5*100: 2/5*180

M+O =120, Now we have to bring this quantity down to 66, 120-66 = 54
therefore, 54/120 = 45%

C is the answer.
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Why are you dividing over 120 and not 180

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2/5 th of mixture of milk and water is replaced by orange juice and 23 Feb 2025, 13:55
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I believe that is because when we remove a percentage of the final mixture (as asked for in the question), it will remove an equal percentage of the sub-parts. For eg:
If we assume Total = 100 and split into 2 parts (70+30). Now when we remove 10% of 100, we are removing [(10% of 70) + (10% of 30)].

In essence, we are not removing just 54 from the mixture, we are removing (54 + some percentage of water) as well. Therefore, we take only the quantity of (milk + orange) as denominator.

Hope this helps.
Sazimordecai
Ankur17000
Mugdho
2/5 th of mixture of milk and water is replaced by orange juice and the ratio of Milk, Water and Orange juice in the resulting mixture becomes 4:5:6 respectively. Initial quantity of milk in the mixture is 20 litres less than that of water. Then What % of resulting mixture should be taken out, due to which total quantity of milk and orange juice in the final mixture becomes 66 litres ?

A. 35%
B. 55%
C. 45%
D. 72%
E. 64%

­Just wanted to add that if all terms in a ratio are multiplied or divided by the same number the ratio will remain the same.

Since M:W:O --> 4:5:6 and M and W as a quantity was reduced to 3/5, then the initial ratio of M:W will also be 4:5

Now that you know 4x = 5x - 20, x = 20
So, initial mixture would be 180, M:W --> 80:100
Now the current mixture would then M:W:O be 3/5*80: 3/5*100: 2/5*180

M+O =120, Now we have to bring this quantity down to 66, 120-66 = 54
therefore, 54/120 = 45%

C is the answer.



Why are you dividing over 120 and not 180

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