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April 14th, 2018, 07:15 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 183 Thanks: 1  I have two doubts in this solution
A mixture of a certain quantity of milk with 16 litres of water is worth 90p per litre. if pure milk be worth Rs.1.08 per litre, how much milk is there in the mixture ? Solutions: By the alligation rule, milk and water are in the ratio of 5 : 1 quantity of milk in the mixture = 5 x 16 = 80. I have two doubts in this solution, How 1.08 is written as 108? Another question: why 5 x 16 why not $16\dfrac {5}{6}$ where 6 is total, 5+1=6? 
April 15th, 2018, 02:47 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,089 Thanks: 846 
I presume there are 100 pence per Rupee so that 1.08 Rps is the same as 108 p. Are you mixing Indian Rupees with British pence? "quantity of milk in the mixture = 5 x 16 = 80." 80 what? There were only 16 liters of mixture so certainly you cannot mean 80 liters of milk in the mixture! You are correct that this should be $\displaystyle \frac{5}{6}(16)$ liters! The mixture is worth $\displaystyle \frac{90}{108}= \frac{45}{54}= \frac{5}{6}$ what pure milk is so there is $\displaystyle \frac{5}{6}(16)= \frac{40}{3}$ liters of milk in the mixture. 
April 15th, 2018, 04:37 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,838 Thanks: 1564 
I assume Country Boy misread the description, as 16 l is the volume of water in the mixture, not the volume of the mixture. If 1 Rs = 100p (p for paisa), the quantity of milk is 80 l, because 96 l of mixture at 0.90 Rs / l is worth 86.4 Rs, and 80 l of milk at 1.08 Rs / l is also worth 86.4 Rs. 
April 15th, 2018, 05:24 AM  #4  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,074 Thanks: 794  Quote:
If pure milk is worth 1.08 per litre, how much pure milk is there in the mixture ? Code: M : 1.08 16 : 0 (unless you buy bottled water!)  M+16 : .90 1.08M = .90(M + 16) M = 80  
April 15th, 2018, 05:58 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,838 Thanks: 1564  The reason was given earlier in your post: "By the alligation rule, milk and water are in the ratio of 5 : 1" and this is obtained from the figures in the image posted... (90  0):(108  90) = 90:18 = 5:1. Hence the quantity of milk = 5 × the quantity of water = 5 × 16 l = 80 l. 
April 15th, 2018, 11:13 AM  #6  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,089 Thanks: 846  Quote:
 

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