If the price of onion increases by 25%, then by what percentage should a family decrease their onion consumption so that their expenditure on onion remains the same?

The correct option is 20%.

Step-by-step Explanation:

Let the initial price of onions be $P$ and the initial consumption of onions be $C$.

The total expenditure on onions is given by the formula:
$\text{Expenditure}=P\times C$

Step 1: Calculate the new price after an increase of 25%
New Price, $P_{\text{new}}=P+0.25P=1.25P$

Step 2: Determine the new consumption needed to keep expenditure constant
Let the new consumption be $C_{\text{new}}$.
Since expenditure must remain the same:
$P_{\text{new}}\times C_{\text{new}}=P\times C$

Substitute $P_{\text{new}}=1.25P$ into the equation:
$1.25P\times C_{\text{new}}=P\times C$

Divide both sides by $P$:
$1.25C_{\text{new}}=C$

Solve for $C_{\text{new}}$:
$C_{\text{new}}=\frac{C}{1.25}=0.8C$

Step 3: Calculate the percentage decrease in consumption
The decrease in consumption is:
$C-C_{\text{new}}=C-0.8C=0.2C$

Percentage decrease in consumption:
$\text{Percentage Decrease}=\left(\frac{0.2C}{C}\right)\times 100=20\%$

Therefore, the family should decrease their onion consumption by 20% so that their expenditure remains the same.