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April 12th, 2018, 03:19 AM   #1
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What is the quantity of milk in the solution?

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?

I tried:

Concentration - Water added - Milk:

100 - 0 - 10 liter

85 - 0 - ?

$\displaystyle \frac {85\times10}{100} = 8.5$

But Answer is 9 litres. Please tell how to solve this problem?

Last edited by Ganesh Ujwal; April 12th, 2018 at 03:23 AM.
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April 12th, 2018, 03:50 AM   #2
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$\displaystyle M$ = amount of milk

$\displaystyle \dfrac{M}{10} - \dfrac{M}{12}= 0.15$
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April 12th, 2018, 03:51 AM   #3
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Quote:
Originally Posted by Ganesh Ujwal View Post
Concentration - Water added - Milk:
Not possible, concentration and water/milk added have different units. You got to respect your units! Concentration is dimensionless, while water/milk added is liters.

Try again!
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April 12th, 2018, 03:55 AM   #4
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Quote:
Originally Posted by mrtwhs View Post
$\displaystyle M$ = amount of milk

$\displaystyle \dfrac{M}{10} - \dfrac{M}{12}= 0.15$
Amount of milk is already given, It is 10. Why you assume M as Amount of milk?
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April 12th, 2018, 04:01 AM   #5
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Quote:
Originally Posted by Ganesh Ujwal View Post
Amount of milk is already given, It is 10. Why you assume M as Amount of milk?
No, amount of milk is not given. The original amount of milk solution (=mixture of milk and water) is given.
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April 12th, 2018, 04:05 AM   #6
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Quote:
Originally Posted by Micrm@ss View Post
No, amount of milk is not given. The original amount of milk solution (=mixture of milk and water) is given.
Why M/10 instead of M X 10?
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April 12th, 2018, 04:06 AM   #7
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Because concentration is defined as
$$\text{concentration} = \frac{\text{Amount of milk}}{\text{Total amount of liquid}}$$
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April 12th, 2018, 05:37 AM   #8
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The question is ambiguous. Does 15% mean 15% of the total quantity of liquid or 15% of the previous concentration or something else?
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April 12th, 2018, 08:24 AM   #9
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I understand this fractions very well $\frac {M}{10}$ and $\frac {M}{12}$

But how this step is obtained: $\displaystyle \frac {M}{10} - \frac {M}{12} = 0.5$ ?

Why negative sign is used?

Last edited by Ganesh Ujwal; April 12th, 2018 at 08:26 AM.
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April 12th, 2018, 10:08 AM   #10
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First, it is 0.15 not 0.5. You said 15% not 50%.

Let $\displaystyle M$ = the amount of milk you have at the start.

The the % of milk in the original 10 liters is $\displaystyle \dfrac{M}{10}$. Notice that if all 10 liters are milk then you have $\displaystyle \dfrac{10}{10}=100\%$ milk but the final answer implies that this is impossible.

You then add 2 liters of water giving you a total of 12 liters of liquid of which you still have $\displaystyle M$ liters of milk since you added water and no milk. Therefore the % of the new liquid which is milk is $\displaystyle \dfrac{M}{12}$. You said that the % of milk went down by 15% so ...

$\displaystyle \dfrac{M}{10}-\dfrac{M}{12}=0.15$ and $\displaystyle M=9$.
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