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.)

Question

Accepted Answer

Let the price of wheat per kg be W. Then price of rice per kg = 0.2W.

Monthly consumption:
Rice = 20 kg
Wheat = 8 kg

Total expenditure = ₹300

Expenditure on rice = 20 × 0.2W = 4W
Expenditure on wheat = 8 × W = 8W

Total expenditure = 4W + 8W = 12W = 300
=> W = 300 / 12 = ₹25 per kg (price of wheat)

Price of rice = 0.2 × 25 = ₹5 per kg

Now, price of wheat increases by 20%:
New price of wheat = 25 × 1.2 = ₹30 per kg

Expenditure on wheat (consumption constant) = 8 × 30 = ₹240

Total expenditure must remain ₹300, so expenditure on rice = 300 - 240 = ₹60

Price of rice remains ₹5 per kg, so new quantity of rice = 60 / 5 = 12 kg

Original rice consumption = 20 kg
New rice consumption = 12 kg

Percentage reduction = ((20 - 12) / 20) × 100 = (8 / 20) × 100 = 40%

Hence, the required percentage reduction in rice consumption is 40%.

Answer

Answer

Answer