If the price of sugar is raised by 25%, find by how much percent a householder must reduce his consumption of sugar so as not to increase h…

Let the initial cost price of one Kg sugar be Rs. X and the quantity initially purchased be Y kgs.

Then, the expenditure for Y kgs of sugar initially

E = X × Y

Since the price goes up by 25%, thus the new price of sugar

$(= {\rm{X}} + {\rm{}}\frac{{25}}{{100}} \times X)$

= 1.25X

Also let the quantity of sugar purchased after increase in price be Y’ kgs.

∴ New expenditure, E’ = 1.25X × Y’

According to question, E = E’

Replacing the value of E and E’ from above we get,

⇒ X × Y = 1.25X × Y’

⇒ Y’ = Y/1.25

Now, reduction in consumption of sugar

= Y – Y’

Reduction percentage

$(= \frac{{Y - Y'}}{Y} \times 100)$

Putting Y’ = Y/1.25 we get,

Reduction percentage

$(= \frac{{Y - \frac{Y}{{1.25}}}}{Y} \times 100)$

= 20%

∴ There must be reduction of 20% consumption in order to ensure same expenditure.