Question

# The price of sugar has increased by $20\%$. As a result, a family decreases its consumption by $25\%$. The expenditure of the family on sugar will be decreased byA. $10\%$ B. $5\%$ C. $14\%$ D. $15\%$

Hint: Let us take the price of sugar as Rs. 100 and then we can use the formula - Expenditure = Price $\times$ Quantity. To calculate the percentage decrease in the expenditure of the family, we can use the formula - change in percentage = change in amount/initial amount $\times$ 100.

Before proceeding with the question, we must have proper knowledge of percentage. We must know the formula - Expenditure = Price $\times$ Quantity to calculate the expenditure.
In this question, we have been given that the price of sugar has increased by $20\%$. As a result of which, a family decreases its consumption by $25\%$. Then, we have been asked to calculate by what percentage the expenditure of the family on sugar will be decreased.
Let us assume that the price of sugar is Rs. 100. So, we can say that before increment in the price, the quantity consumed by the family is $100\%$.
As we know that the Expenditure = Price $\times$ Quantity, we can write the expenditure of the family as
$\Rightarrow 100\times 100=10000$
Therefore, the expenditure of the family before increasing the price is Rs. $10000$.
As the sugar cost increases by $20\%$, we can write that the cost of sugar is $20\%\text{ of }100$.
The new price of the sugar is equal to $100+20\%\text{ of }100=100+\dfrac{20}{100}\times 100$.
Therefore, the new price of sugar is Rs. 120.
Again, we know that the Expenditure = Price $\times$ Quantity. Here, it is given that the expenditure decreases by $25\%$, it means the quantity used by the family is $\left( 100-25 \right)\%=75\%$.
So, the expenditure becomes $=120\times 75$.
Therefore, the new expenditure of the family is $9000$.
Now, we have to find the decrease in the percentage of the expenditure and we know that the change in percentage is = change in amount/initial amount $\times$ 100.
$\therefore$ change in the amount $=(10000-9000)=1000$
Decreased percentage of expenditure is $=\dfrac{1000}{10000}\times 100$
Therefore, the decreased percentage of expenditure is $=10\%$.
Hence, the correct answer is option A.

Note: We must always suppose the price of the sugar as Rs. 100 instead of supposing it as a variable x. This will make the calculation easy to understand. The formula for change in percentage is given by the change in amount/initial amount $\times$ 100. There is a possibility that the student uses the inverse of the formula and ends up getting the wrong answer.