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August 2nd, 2019, 10:05 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 476 Thanks: 1  Solve this two doubts in mixture problem.
A can contains a mixture of two liquids A & B in the ratio 7:5 When 9 liters of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. Liters of liquid A contained by the can intially was? Solution: A:B Ratio 7:5 A:B = 7:9 4===9 16===36*7/12=21 How 4 corresponds to 9? Why 4 is multiplied both sides to get 16 & 36 in last step? 
August 2nd, 2019, 01:14 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
The 7:5 ratio represents 7(9/4)L:5(9/4)L, which total 12(9/4)L. (The 9/4 comes from 9/(9  5).) To get the original volumes, one scales up by (12(9/4) + 9)/(12(9/4)), which is 4/3. Hence the original volume of A was 7(9/4)(4/3)L = 7(36/12)L = 21L. The above explains everything except the "16" in the last line of the solution. I'm not sure why it's there. 
August 2nd, 2019, 08:09 PM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 476 Thanks: 1  
August 3rd, 2019, 04:38 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
The 9 is because 9L of liquid B are added. The 4 is because the A:B ratio changes from 7:5 to 7:9 and 9  5 = 4. Multiplying both numbers in the ratio by 9/4 doesn't change the ratio, but changes the increase in the second value from 4 to 9. The numbers used for the ratio have therefore become the numbers of Liters of liquids A and B. 
August 4th, 2019, 03:16 AM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 476 Thanks: 1  
August 4th, 2019, 10:55 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
The 7:5 ratio becomes written as (63/4):(45/4). The 7:9 ratio becomes written as (63/4):(81/4). Now 45/4 + 9 = 81/4, and clearly any factor other than 9/4 wouldn't achieve that. Hence (63/4)L and (45/4)L are the volumes immediately prior to 9L of liquid B being added. 

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