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.)
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 40%.
Given that, price of rice = 20% of price of wheat
Total expenditure on rice and wheat per month = ₹300
Let the price of wheat be ₹5x.
⇒ Price of rice = 20% of 5x
⇒ × x
⇒ (5x) = x
According to the given question,
⇒ 20x + 8(5x) = 300
⇒ 20x + 40x = 300
⇒ 60x = 300
⇒ x = 5
Now, price of wheat = 5x = 25
Also, the price of wheat is increased by 20%.
New price of wheat =
⇒ 30
Let the new consumption of rice be y kg.
⇒ 8 × 30 + 5y = 300
⇒ 240 + 5y = 300
⇒ 5y = 60
⇒ y = 12
Difference in the consumption of rice = 20 - 12 = 8 kg
Now, percentage reduction in consumption of rice =
⇒ 8 × 5 = 40%
Hence the required answer is 40%.