Every month, a man consumes 20 kg of rice and 8 kg of wheat. The price of rice is 20% of the price of wheat, resulting in a total expenditure of ₹300 per month for rice and wheat combined. If the price of wheat is increased by 20%, what percentage reduction in rice consumption is needed to maintain the same expenditure of ₹300? (Given that price of rice and consumption of wheat is constant.)

Rice consumption = 20 kg/month
Wheat consumption = 8 kg/month

Total expenditure on rice and wheat = ₹300/month

Price of rice = 20% of the price of wheat

Price of wheat increases by 20%

Price of rice and consumption of wheat remain constant

Let the price of the wheat is ₹x.

Then, price of rice = ₹0.2x

According to the question,

​$$20\times 0.2x + 8\times x = 300 \\4x + 8x = 300 \\12x = 300 \\x = \frac{300}{12} = ₹25$$​​

Price of wheat = ₹25

Price of rice = $$25 \times 0.2 = ₹5$$​​

Now, the price of the wheat is increased by 20%

New price of the wheat = $$25 \times \frac{120}{100} = ₹30$$​​

New expenditure on wheat = $$30 \times 8 = ₹240$$​​

Total Expenditure remains the same (₹300)

Remaining = 300 – 240 = ₹60

New consumption on rice = $$\frac{60}{5} = 12 kg$$​​

Reduction(%) in the consumption of rice = $$\frac{20 -12}{20}\times 100 = 40 \%$$​​