April 12th, 2018, 02:19 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 294 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: 682 Thanks: 129 
$\displaystyle M$ = amount of milk $\displaystyle \dfrac{M}{10}  \dfrac{M}{12}= 0.15$ 
April 12th, 2018, 02:51 AM  #3 
Senior Member Joined: Oct 2009 Posts: 428 Thanks: 144  
April 12th, 2018, 02:55 AM  #4 
Senior Member Joined: Aug 2014 From: India Posts: 294 Thanks: 1  
April 12th, 2018, 03:01 AM  #5 
Senior Member Joined: Oct 2009 Posts: 428 Thanks: 144  
April 12th, 2018, 03:05 AM  #6 
Senior Member Joined: Aug 2014 From: India Posts: 294 Thanks: 1  
April 12th, 2018, 03:06 AM  #7 
Senior Member Joined: Oct 2009 Posts: 428 Thanks: 144 
Because concentration is defined as $$\text{concentration} = \frac{\text{Amount of milk}}{\text{Total amount of liquid}}$$ 
April 12th, 2018, 04:37 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,174 Thanks: 1644 
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: 294 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: 682 Thanks: 129 
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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