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In a milk solution of 10 lit, 2 lit of water is added thereby the concentration of milk is reduced by 15%. What is the quantity of milk in the solution? (Ans is 9)

I tried:

Concentration - Water added - Milk:

100 - 0 - 10 liter

85 - 0 - ?

$\dfrac {85\times10}{100} = 8.5$

Then my friend showed me this formula: $\dfrac{M}{10}-\dfrac{M}{12}=0.15$

How can he be so sure that difference between $\dfrac{M}{10}$ and $\dfrac{M}{12}$ is 0.15 if they are so many possibilities:

1) 0.15 + $\dfrac{M}{10} = \dfrac{M}{12}$

2) Question used the word "added" so why not this equation: $\dfrac{M}{10} + \dfrac{M}{12}$ = 0.15.

Siberan Jonah
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1 Answers1

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Your friend is right. Let $M$ be the amount of milk. At first, the percentage of milk is $\frac M{10}$.

Now we add $2$ litres of water, so the new percentage of milk is $\frac M{12}$. We are told that this is $15\%$ less than before, so

$$\frac M{12} = \frac M{10} - 0.15.$$

(This is effectively the same formula as your friend's, but personally I find it makes more sense to put $\frac M{12}$ on the left-hand side.}

As for your question #2 ("why not $\frac M{10} + \frac M{12} = 0.15$"), that formula doesn't really make sense. What's being added is water (hence the denominator increasing from $10$ to $12$), not the percentage of milk.

Théophile
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  • why $\dfrac {M}{10 %}$ instead of $\dfrac {10 %}{M}$? – Siberan Jonah Apr 13 '18 at 03:39
  • @SiberanJonah The total quantity of liquid is $10$ litres. Part of that is milk, $M$. The fraction $M/10$ represents how much of the total is milk. If $M=1$, for example, $0.1$ (or $10%$) of the total is milk. – Théophile Apr 15 '18 at 04:05