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.
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.