Question

A can contains milk and water in the ratio 3:1. a part of this mixture is replaced with milk, and now the new ratio of milk to water is 15:4.what proportion of original mixture had been repla

Answer 1

3/19th part of the whole mixture is replaced

Answer 2

If the new ratio of milk to water is 15:4, then the proportion of the original mixture that had been replaced is 3/19.

Step-by-step explanation:

The initial ratio of milk and water in the can = 3:1

The new ratio of milk to water = 15:4

Let the original mixture be "x" litres and let “y” litres of the mixture is replaced with “y” litres of milk.

So,  

After y litres of mixture is drawn out,  

The quantity of milk becomes = $[\frac{3}{3+1} *x] - [\frac{3}{3+1} * y] = \frac{3x}{4} - \frac{3y}{4}$

and,

The quantity of water becomes = $[\frac{1}{3+1} * x ] - [\frac{1}{3+1} * y] = \frac{x}{4} - \frac{y}{4}$

Also,  

“y” litres of milk poured in can, therefore,

The final quantity of milk becomes = $\frac{3x}{4} - \frac{3y}{4} + y = \frac{3x}{4} + \frac{y}{4}$

Now, according to the question, we can finally write the eq. as,

$\frac{\frac{3x}{4} + \frac{y}{4}}{\frac{x}{4} - \frac{y}{4}} = \frac{15}{4}$

⇒ $\frac{3x + y}{x - y} = \frac{15}{4}$

⇒ 4[3x+y] = 15[x-y]

⇒ 12x + 4y = 15x – 15y

⇒ 19y = 3x

⇒ y = $\frac{3}{19}$ * x

Thus, $\frac{3}{19}$ proportion of original mixture had been replaced.

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