Question

If the price of tea rises by 20%, then by how much percent does a housewife reduce her consumption so that her expenditure remains the same?
\[\begin{align}
  & A.20\% \\
 & B.12\dfrac{1}{2}\% \\
 & C.\dfrac{50}{3}\% \\
 & D.\dfrac{50}{6}\% \\
\end{align}\]

Answer 1

Hint: In this question, we are given the percentage increase in the price of tea. We need to find the percentage of the consumption that has to be reduced so that expenditure remains the same. For this, we will take the original price of the tea as Rs.100 and then evaluate the extra cost increased. Now increase cost should be decreased from total cost. So we will find that percentage using $\dfrac{\text{Increase in cost}}{\text{New cost}}\times 100$. It will give us our required answer.

Complete step-by-step answer:
Here we are given that, the price of tea rises by 20%. Let us suppose that the original price of the tea was Rs.100. Now we need to find the new price of the tea. For this, we will use the formula: $\text{Original price}+\dfrac{\text{Percentage increased}}{100}\times \text{Original price}$.
Hence, the new price of tea becomes $\Rightarrow 100+\dfrac{20}{100}\times 100=100+20=Rs.120$.
So, the new price of tea becomes Rs.120 if the original price was Rs.100.
We can say increase in price will be equal to: New price - original price.
$\Rightarrow Rs.120-Rs.100=Rs.20$.
Now, Rs.20 would be increased in expenditure but we need to reduce the consumption so that expenditure remains the same. Hence, we have to reduce tea cost Rs.20 out of the new cost of Rs.120.
So, percentage decreased would be given by $\dfrac{\text{Increase in cost}}{\text{New cost}}\times 100$.
\[\begin{align}
  & \Rightarrow \dfrac{20}{120}\times 100 \\
 & \Rightarrow \dfrac{2000}{120} \\
 & \Rightarrow \dfrac{200}{12} \\
 & \Rightarrow \dfrac{50}{3}\% \\
\end{align}\]
Hence the consumption of $\dfrac{50}{3}\%$ of tea is to be decreased so that the expenditure on tea remains the same.

So, the correct answer is “Option C”.

Note: Students can take any value as an actual price. We have taken Rs.100 to make our calculations easy. Students can make the mistake of taking a decrease in price by the original price. But we have to decrease the consumption from new prices only.