The expenditure on food is 35% of the income of a particular family. If the income is raised by 30%, then how much percentage (to the nearest whole number) of food expenditure is less than the initial percentage to keep the food expenditure unchanged?

23

Let Total Income = 100x

Expenditure on food = 35% of 100x = 35x

Increased Income = 100x + 30% of 100x = 130x

As, Expenditure is same as before . i.e. 35% of Income

Expenditure = 35% of 130x  = 45.5x

Required percentage = \(\frac{45.5x - 35x }{45.5x}\) × 100

= 23.07 %

= 23.07% (approx)