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 :

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?

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?

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?