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Home->Aptitude->Alligation or Mixture ->Formula/Rule 12

Alligation or Mixture :-

    Direct Formula / Rule 12 :

  • Theorem: A person's expenditure and savings are in the ratio a : b. His income increases by x%. His expenditure also increases by y%. His percentage increase in saving is given by
    = [ ( a + 1 ) x - a y ] %
    bb

  • Example :

  • Mira's expenditure and saving are in the ratio 3 : 2 Her income increases by 10%. Her expenditure also increases by 12%. By how many % does her saving increase?

  • Detail Method :
    Let the Mira's expenditure and saving be Rs 3x and Rs 2x
    Mira's income = 3x + 2x = 5x
    Increased income = 5x X 110 = 11 x
    1002
    Increased expenditure = 3x X 112 = 84 x
    10025
    Increased saving = 11 x - 84 x = 107x
    22550
    Increase in saving = 107x - 2x = 7x
    5050
    % increase in saving = 7x X 100 = 7%
    50 X 2x

  • Ailigation Method :

    Expenditure Saving
    (as there is loss on the whole)
    12
    (% increase in exp)
           10
    (% increase in income)
    x
    (% increase in saving)
    3 2(given)
    We get two values of x, 7 and 13. But to get a viable answer we must keep in mind that the central value (10) must lie between x and 12. Thus the value of x should be 7 and not 13.
    So required % increase = 7%

  • Quicker Method : Here you can use direct formula :
    the required percentage increase in saving
    = [ ( 3 + 1 ) X 10 - 3 X 12 ] = 25 - 18 = 7%.
    22


    Exercise :
  1. Ritu's expenditure and saving are in the ratio 5 : 2. Her income increases by 12%. Her expenditure also increases by 14%. By how many % does her saving increase?
  2. Sita's expenditure and saving are in the ratio 5 : 3. Her income increases by 15%. Her expenditure also increases by 9%. By how many % does her saving increase?
  3. Ranju's expenditure and saving are in the ratio 4 : 5. Her income increases by 25%. Her expenditure also increases by 35%. By how many % does her saving increase?
  4. Answers : 1 = 7%,   2 = 25%,   3 = 17%