Alligation or Mixture -> Formula/Rule 5

Direct Formula / Rule 5 :
• Theorem: n gm of sugar solution has x% sugar in it. The quantity of sugar should be added to make it y% in the solution is given by

  = n	(	y - x	)	gm.
  		100 - y

  or Quantity of sugar added

  =	(	Solution (required % value - present % value)	)
  		(100 - required % value)
• Example :
300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution?
• Detail Method : 
  300 X 40/100 = 120 gm
  300 - 120 = 180 gm
  180gm = 120 + 60 gm
  so 60 gm 
• Ailigation Method : 
  The existing solution has 40% sugar. And sugar is to be mixed; so the other solution has 100% sugar. So by alligation method:

  40%		50%		100%
  50%				10%

  The two mixtures should be added in the ratio 5 : 1.
  

  Therefore, required sugar =	300	X 1 = 60 gm.
  	5
• Quicker Method : Here you can use direct formula : 

  quantity of sugar added =	300 (50 - 40)	= 60 gm.
  	100 - 50

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Exercise :
1. A mixture of 40 litres of milk and water contains 10% water. How much water must be added to make 20% water in the new mixture?
2. A petrol pump owner mixed leaded and unleaded petrol in such a way that the mixture contains 10% unleaded petrol. What quantity of leaded petrol should be added to 1 litre mixture so that the percentage of unleaded petrol becomes 5%.
3. 15 litres of a mixture contains 20% alcohol and the rest water. If 3 litres of water be mixed in it, the percentage of alcohol in the new mixture will be: 
Answers : 1 = 5 litres,   2 = 1000 ml,   3 = 16 2/3%