A woman spends 2/3 of her income. If her income increases by 18% and the expenditure increases by 24% then the percentage increase in her savings will be:

Options
a) 3%
b) 6%
c) 4%
d) 5%

Solution

Let the Income = x
Expenditure = $ \frac{2}{3}x $
Saving = $ \frac{1}{3}x $
Income increases 18% = $ x + \frac {x \times 18}{100} = \frac{118x}{100}$
Expenditure increases 24% = $ \frac{2}{3}x + \frac{2}{3}x \times \frac{24}{100}$

Expenditure increases 24% = $ \frac{2}{3}x + \frac{16x}{100} = \frac{200x + 48x}{300} = \frac{248x}{300}$
New saving = Income – Expenditure
New saving = $ \frac{118x}{100} – \frac{248x}{300} = \frac{354x – 248x}{300} = \frac{106x}{300}$

Income in saving = $ \frac{106x}{300} – \frac{1}{3}x = \frac{(106 – 100)x}{300} = \frac{6x}{50}$

% Income saving = $ \dfrac{\frac{x}{50}} {\frac{1}{3}} \times 100 $ = 6%

Answer: 6%