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# 2/5 th of mixture of milk and water is replaced by orange juice and

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Re: 2/5 th of mixture of milk and water is replaced by orange juice and [#permalink]
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chetan2u wrote:
Mugdho wrote:
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

Why is 54/120 and not 54/180?

Thank you
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Re: 2/5 th of mixture of milk and water is replaced by orange juice and [#permalink]
KarishmaB ma'am can you kindly help to solve this.
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2/5 th of mixture of milk and water is replaced by orange juice and [#permalink]
chetan2u wrote:
Mugdho wrote:
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

chetan2u

­I am confused how you are getting 25x/3 and 20x/3­
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Re: 2/5 th of mixture of milk and water is replaced by orange juice and [#permalink]
Expert Reply
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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Re: 2/5 th of mixture of milk and water is replaced by orange juice and [#permalink]
Expert Reply

Mugdho wrote:
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 ?

­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%
Re: 2/5 th of mixture of milk and water is replaced by orange juice and [#permalink]
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