Question

due to an increase in the price of sugar by 25% by how much a householder decrease the consumption of sugar so that there is no increase in the expenditure on sugar

Answer 1

$\large\bold{\boxed{Solution :} }$

$\blue{Let \: \: consumption \: \: of \: \: sugar \: \: originally}$
$\blue{be \: \: 1 \: \: unit \: \: and \: \: cost \: \: of \: \: 1 \: \: unit}$
$be \: \red{ Rs} \: \: 100$

$\blue{But \: \: now \: \: cost \: \: of \: \: 1 \: \: unit \: = 100 + 25}$
$= 125$

$Now \: \red{ Rs} \: \: 100 \: \: be \: \: the \: \: cost \: \: of \: \: 1$
$unit \: \: \: sugar$

$\red{Rs} \: \: 1 \: \: be \: \: the \: \: cost \: \: of \: \: \frac{1}{125} \: \: unit \: \:$
$sugar$

$\red{Rs }\: \: 100 \: \: be \: \: the \: \: cost \: \: of \: \: \frac{1}{125} \times 100$
$= \frac{4}{5} \: \: unit \: \: sugar$

$\blue{Reduction \: \: \: of \: \: \: consumption}$

$\red{ = 1 - \frac{4}{5}}$

$\blue{ = \frac{5 - 4}{5} }$

$\red{ = \frac{1}{5} \: \: unit}\\ \: \:$

$\blue{Required \: \: percent \: of \: \: reduction}$

$\red{ = \frac{1}{5 \times 1} \times 100 \%}$

$\red{ = \frac{100}{5} \%}$

$\red{ = 20\% }\: \: \large\bold{\boxed{ Ans}}$