Question

The price of an article is increased by 20%. By what percentage must its consumption be reduced so that the expenditure on it reduces by 10%?​

Answer 1

Let the initial price of article be 100x and initial consumption be y.

Expenditure=price*consumption(eq.1)

=100xy

Since price increases by 20%,

New price= 100x +20%of 100x

=100x+20x

=120x

Let new consumption be y'.

Given expenditure reduces by 10%,

New expenditure= 100xy-10%of100xy

=90xy

Putting it into eq.1,

90xy=120xy'

3/4y=y'

therefore, new consumption=3/4y

change in consumption=initial consumption-new consumption

=y-3/4y

=1/4y

putting it into %age form: (1/4y)/y*100

=25%