The ratio of expenditure and savings is 3 : 2. If the income increases by 15% and the savings increase by 6%, then by how much percent should his expenditure increase?

Question: The ratio of a person’s expenditure to savings is 3 : 2. If his income increases by 15% and his savings increase by 6%, by what percentage will his expenditure increase?

Solution:
Let the original expenditure be 3x and the original savings be 2x.

∴ the original income
= 3x + 2x
= 5x

After a 15% increase, the new income
= 5x × (115/100)
= 5.75x

After a 6% increase, the new savings
= 2x × (106/100)
= 2.12x

∴ new expenditure
= New income - New savings
= 5.75x - 2.12x
= 3.63x

Increase in expenditure
= 3.63x - 3x
= 0.63x

Therefore, the percentage increase in expenditure
= (0.63x/3x) × 100%
= 21%