Question

The price of sugar is increased by 20%. As a result, a family decreases its consumption by 25%. The expenditure of the family on sugar will be decreased by

Answer 1

Hint: The expenditure of the family on sugar is equal to the product of the current price of sugar and the amount of sugar consumed or the consumption.
The formula for finding x percentage of any quantity 1 is
\[\dfrac{x}{100}\times Quantity\ 1\]
The formula to calculate the change percentage for a quantity is given as follows
\[change\ percentage=\dfrac{final\ value-initial\ value}{initial\ value}\times 100\]

Complete step-by-step answer:
As per the question, let the initial cost of sugar be Rs. X/kg and the initial consumption of sugar be y kg.
Using the formula given in the hint, the initial expenditure of the family on sugar is
\[=Rs.x\cdot y\]

Now, as mentioned in the question, the price of sugar is increased by 20% and subsequently, the family decreases its consumption by 25%, therefore
Final price of sugar is
\[\begin{align}
  & =x+\dfrac{20}{100}\times x \\
 & =Rs.\dfrac{6x}{5}/kg \\
\end{align}\]

And the final consumption of the family is
\[\begin{align}
  & =y-\dfrac{25}{100}\times y \\
 & =\dfrac{3y}{4}\ kg \\
\end{align}\]

Hence, the new expenditure of the family on sugar is
\[\begin{align}
  & =\dfrac{6x}{5}\cdot \dfrac{3y}{4} \\
 & =Rs.\dfrac{9x\cdot y}{10} \\
\end{align}\]

Now the change % can be calculated as
\[\begin{align}
  & =\dfrac{final\ value-initial\ value}{initial\ value}\times 100 \\
 & =\dfrac{\dfrac{9x\cdot y}{10}-x\cdot y}{x\cdot y}\times 100 \\
 & =-\dfrac{1}{10}\times 100 \\
 & =-10 \\
\end{align}\]
Hence, the decrease in the expenditure of the family on sugar is by 10%.

Note: The only step at which the student can make an error is where the expenditure is to be calculated which is by using the formula as given in the hint. The expenditure of the family on sugar is equal to the product of the current price of sugar and the amount of sugar consumed or the consumption.