A sample of x litres from a container having a 60 litre mixture of mil

Question

A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

A. 6 litres

B. 10 litres

C. 30 litres

D. 32 litres

E. 35 litres

Show Answer

Official Answer

B

A. 6 litres

B. 10 litres

C. 30 litres

D. 32 litres

E. 35 litres

pahujagagan5 · Accepted Answer

A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

A. 6 litres

B. 10 litres

C. 30 litres

D. 32 litres

E. 35 litres

Show Answer

Official Answer

B

A. 6 litres

B. 10 litres

C. 30 litres

D. 32 litres

E. 35 litres

We have 60 litres of the mixture containing milk and water in the ratio 2:3. So we have 24 litres of Milk and 36 litres of water in the mixture.

Now we have to replace x litres of mixture with pure milk so that both the constituents are in equal proportions.

For every 1 litre of the mixture that we remove, we add 0.6 litres of milk and remove 0.6 litres of water. So we can form the equation :

24 + 0.6x = 36 - 0.6x
 1.2x = 12
 x = 10 Litres

If we remove 10 litres of mixture, we will be left with a solution containing 20 litres of milk and 30 litres of water. Now if we add 10 litres of pure milk to the mixture, we will have 30 litres of each constituent.

Hope this helps.

Posted from my mobile device

Kinshook · Answer

Given: A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions.
Asked: What is the value of x?

Before:
Milk = 24 litres
Water = 36 litres
Solution = 60 litres

After replacement of x litres of solution with milk: - 
Milk = 24 - .4x +x = 24 + .6x
Water = 36 - .6x 
Since milk and water become equal
24 + .6x = 36 - .6x
1.2x = 12
x = 10 litres

IMO B

CEdward · Answer

I always like to hammer it into my brain that for mixture questions (and rate/work problems) that it's all about setting up the equations.

Here the equation is:

(24 - 2/5x + x) / 60 = 1/2
x = 10

Answer is B.

PrekshaashokJain · Answer

we add 0.6 litres of milk and remove 0.6 litres of water. - why 0.6 and not 6 ?

Biswajeet1930 · Answer

can you explain this solution please....

Krunaal · Answer

That is while setting up the equation, since water is  \frac{3}{5} th of the solution, and milk is  \frac{2}{5} th,

Total quantity removed and then replaced is x

\frac{3}{5}*x  = 0.6x => this is the water removed

\frac{2}{5}*x  = 0.4x => this is the milk removed

We replace x quantity (mixture of milk and water) removed with pure milk which is also x in terms of quantity , now since we had removed 0.4x milk, and added x milk => -0.4x + x = 0.6x

Above leads to the equation => 24 + 0.6x = 36 - 0.6x, since after the operation milk and water is equal.

Solving we get x = 10, hence 10 litres of pure milk was added.

Hope it helps.

Krunaal · Answer

When milk and water are equal in 60 litres, fraction of milk in total mixture will be  \frac{1}{2}

Now doing what get's us the fraction of milk =  \frac{1}{2} ?

From existing 24 litres of milk, we first remove  \frac{2}{5} * x  litres of milk, and then add x litres of pure milk =>  24 - \frac{2}{5} * x + x = 24 + \frac{3}{5} * x

(24 + \frac{3}{5} * x)  / 60 =  \frac{1}{2}

Solving, we get  x = 10

Biswajeet1930 · Answer

That has been really helpful, thank you so much

A sample of x litres from a container having a 60 litre mixture of mil

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A sample of x litres from a container having a 60 litre mixture of mil

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