Problem:

A person saves 10% of his income. His income increases by 20% but his saving remains constant. Find the percentage increase in his expenditure?

Solution:

Let the person's income be $100.

He saves 10% of his income, so his savings are $10 and his expenditure is $90.

His income increases by 20%, so his new income is $120.

Since his savings remain constant at $10, his new expenditure is $110.

Therefore, his expenditure has increased by:

$\frac{\text{New expenditure - Old expenditure}}{\text{Old expenditure}}\times100\%$

$=\frac{110-90}{90}\times100\%$

$=22.22\%$

Therefore, the percentage increase in his expenditure is 22.22%.

Explanation:

We are given that a person saves 10% of his income. This means that his expenditure is 90% of his income.

When his income increases by 20%, his new income becomes 120% of his old income.

However, his savings remain constant at 10% of his old income, which means that his new savings are also 10% of his new income.

Therefore, his new expenditure is:

New expenditure = New income - New savings

New expenditure = 120% of old income - 10% of old income

New expenditure = 110% of old income

Therefore, the percentage increase in his expenditure is:

$\frac{\text{New expenditure - Old expenditure}}{\text{Old expenditure}}\times100\%$

$=\frac{110-90}{90}\times100\%$

$=22.22\%$

This means that his expenditure has increased by 22.22%.