Question

If the price of sugar increased by 25%, by how much percent a housewife should reduce the consumption so as not to increase the expenditure.

• A. 25%
• B. 20%
• C. 22.5%
• D. 27.5%

Answer 1

The Correct Option is B

To solve this problem, we need to understand the relationship between price increase, consumption, and expenditure. If the price of sugar increases by 25%, this means that the housewife's original expenditure can continue only if the total money spent remains constant. Thus, if the price goes up by 25%, the consumption must go down so that the product of price and consumption (which gives the expenditure) remains unchanged. Let's denote the original price as \( P \) and the original consumption as \( C \). Therefore, the original expenditure is \( P \times C \). If the price increases by 25%, the new price is \( P+0.25P = 1.25P \). Let the new consumption be \( C' \). The new expenditure shouldn't exceed the original expenditure, hence:

\[1.25P \times C' = P \times C\] 

From this equation, we can solve for \( C' \):

\[C' = \frac{P \times C}{1.25P} = \frac{C}{1.25}\]

Simplifying \(\frac{1}{1.25}\) gives us \(\frac{4}{5}\). Therefore:

\[C' = C \times \frac{4}{5}\]

This means the consumption has to be reduced to \( \frac{4}{5} \) of its original, which is a 20% reduction:

\[ \text{Percentage reduction} = \left(1 - \frac{4}{5}\right) \times 100\% = \frac{1}{5} \times 100\% = 20\%\]

The housewife must reduce the consumption by 20% to keep the expenditure constant when the price increases by 25%.

The correct answer is therefore 20%.