A cup contains milk and water in the ratio of 3:1. How much mixture should be taken out and water added to make the ratio 1:1 ?
Answers
Answer:
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Step-by-step explanation:
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}[
3+1
3
∗x]−[
3+1
3
∗y]=
4
3x
−
4
3y
and,
The quantity of water becomes = [\frac{1}{3+1} * x ] - [\frac{1}{3+1} * y] = \frac{x}{4} - \frac{y}{4}[
3+1
1
∗x]−[
3+1
1
∗y]=
4
x
−
4
y
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}
4
3x
−
4
3y
+y=
4
3x
+
4
y
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}
4
x
−
4
y
4
3x
+
4
y
=
4
15
⇒ \frac{3x + y}{x - y} = \frac{15}{4}
x−y
3x+y
=
4
15
⇒ 4[3x+y] = 15[x-y]
⇒ 12x + 4y = 15x – 15y
⇒ 19y = 3x
⇒ y = \frac{3}{19}
19
3
* x
Thus, \frac{3}{19}
19
3
proportion of original mixture had been replaced.
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