The ratio of expenditure to savings of a woman is 5:1. If her income and expenditure are increased by 10% and 20%, respectively, then find the percentage change in her savings.

40%

Let the initial expenditure be 5R

The final expenditure = 5R x \(\frac{120}{100}\) = 6R (increase of x% = \(\frac{100+x}{100}\))

Initial income = 5R + 1R = 6R

Changed income = 6R x \(\frac{110}{100}\) = \(\frac{33}{5}\)R

Changed savings = Final income - Final expenditure = \(\frac{33}{5}\)R - 6R = \(\frac{3}{5}\)R

% change in savings = \(\frac{change\; in\; savings}{initial\; savings}\)

                              = \(\frac{R - \frac{3R}{5} }{R}\) x 100 =  40%