Question

If the price of tea is raised by 40%,by how much percent must a householder reduce his consumption of tea,so as not to increase his expenditure.Answer step by step​

Answer 1

Statement of the given problem,

If the price of tea increased by 20%, by what per cent must the consumption be reduced to keep the expenses the same?

Let CP1 & CP2 denote respectively initial & increased cost-prices per unit-weight of tea.

Let CN1 & CN2 denote respectively initial & decreased consumption (in unit-weight) of tea.

From above data we get following relations,

CP2 = (1 + 20/100)*CP1 = 1.20*CP1 …… (1a)

CN2*CP2 = CN1*CP1 …… (1b)

From (1b) & (1a) we get,

CN2*1.20*CP1= CN1*CP1

or CN2 = (100/120)*CN1

or CN2 = (1 - 1/6)*CN1

or CN2 = [1 - (100/6)/100]*CN1

or CN2 = (1 - 16.67/100)*CN1 …… (1c)

Therefore from (1c) it is evident that

to keep the expenses the same as before,

the consumption of tea must be reduced by 16.67%. [Ans]