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

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 April 12th, 2018, 03:19 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 343 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 03:23 AM.
 April 12th, 2018, 03:50 AM #2 Senior Member     Joined: Feb 2010 Posts: 702 Thanks: 137 $\displaystyle M$ = amount of milk $\displaystyle \dfrac{M}{10} - \dfrac{M}{12}= 0.15$
April 12th, 2018, 03:51 AM   #3
Senior Member

Joined: Oct 2009

Posts: 733
Thanks: 247

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, 03:55 AM   #4
Senior Member

Joined: Aug 2014
From: India

Posts: 343
Thanks: 1

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, 04:01 AM   #5
Senior Member

Joined: Oct 2009

Posts: 733
Thanks: 247

Quote:
 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, 04:05 AM   #6
Senior Member

Joined: Aug 2014
From: India

Posts: 343
Thanks: 1

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, 04:06 AM #7 Senior Member   Joined: Oct 2009 Posts: 733 Thanks: 247 Because concentration is defined as $$\text{concentration} = \frac{\text{Amount of milk}}{\text{Total amount of liquid}}$$ Thanks from Ganesh Ujwal
 April 12th, 2018, 05:37 AM #8 Global Moderator   Joined: Dec 2006 Posts: 20,288 Thanks: 1968 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, 08:24 AM #9 Senior Member   Joined: Aug 2014 From: India Posts: 343 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 08:26 AM.
 April 12th, 2018, 10:08 AM #10 Senior Member     Joined: Feb 2010 Posts: 702 Thanks: 137 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 $\displaystyle M=9$.

 Tags milk, quantity, solution

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post blimper Algebra 1 August 27th, 2016 12:58 PM Adrian Physics 7 February 14th, 2012 01:10 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top