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Home->Aptitude->Alligation or Mixture ->Formula/Rule 5

Alligation or Mixture :-

    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%