The price of rice is increased by 25%. By what percent should a family decrease its consumption so that their expenditure remains the same?

Correct option is D

Given:

Price of rice increases by 25%

Expenditure must remain constant

Solution:

​​Let, Initial price of rice = ₹1 per kg

Initial consumption = 100 kg
Initial expenditure = ₹1 × 100 = ₹100

Now, price increases by 25%
New price = ₹1 + 25% of ₹1 = ₹1.25 per kg

Let new consumption = x kg
Since expenditure must remain the same (₹100):

​$$1.25 \times x = 100$$​

x $$= \frac{100}{1.25} = 80 \text{ kg}$$​

So, consumption reduced from 100 kg to 80 kg

Decrease = 100 − 80 = 20 kg

Percentage decrease = $$\frac{20}{100} \times 100 = 20\%$$

Alternate Method:

$$\text{Required \% Decrease} = \frac{25}{100 + 25} \times 100 = \frac{25}{125} \times 100 = 20\%$$​​