My Math Forum What is the quantity of milk in the solution?

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 April 12th, 2018, 02:19 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 310 Thanks: 1 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 02:23 AM.
 April 12th, 2018, 02:50 AM #2 Senior Member     Joined: Feb 2010 Posts: 689 Thanks: 131 $\displaystyle M$ = amount of milk $\displaystyle \dfrac{M}{10} - \dfrac{M}{12}= 0.15$
April 12th, 2018, 02:51 AM   #3
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Quote:
 Originally Posted by Ganesh Ujwal 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!

April 12th, 2018, 02:55 AM   #4
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Quote:
 Originally Posted by mrtwhs $\displaystyle M$ = 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?

April 12th, 2018, 03:01 AM   #5
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 Originally Posted by Ganesh Ujwal 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.

April 12th, 2018, 03:05 AM   #6
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Quote:
 Originally Posted by Micrm@ss 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?

 April 12th, 2018, 03:06 AM #7 Senior Member   Joined: Oct 2009 Posts: 519 Thanks: 165 Because concentration is defined as $$\text{concentration} = \frac{\text{Amount of milk}}{\text{Total amount of liquid}}$$ Thanks from Ganesh Ujwal
 April 12th, 2018, 04:37 AM #8 Global Moderator   Joined: Dec 2006 Posts: 19,546 Thanks: 1754 The question is ambiguous. Does 15% mean 15% of the total quantity of liquid or 15% of the previous concentration or something else?
 April 12th, 2018, 07:24 AM #9 Senior Member   Joined: Aug 2014 From: India Posts: 310 Thanks: 1 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 07:26 AM.
 April 12th, 2018, 09:08 AM #10 Senior Member     Joined: Feb 2010 Posts: 689 Thanks: 131 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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