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

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 ] % b b

• 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 100 2
 Increased expenditure = 3x X 112 = 84 x 100 25
 Increased saving = 11 x - 84 x = 107x 2 25 50
 Increase in saving = 107x - 2x = 7x 50 50
 % 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%. 2 2

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%

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