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 Alligation or Mixture :-
 ::Important Formulas ::Examples

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

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:
4. Answers : 1 = 5 litres,   2 = 1000 ml,   3 = 16 2/3%

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