If the price of a commodity is increased by 40 %, then by what proportion must its consumption be reduced so as to maintain the same expenditure on its consumption?
Short Trick: Since the price of the commodity is increased by 40% and expenditure has to be the same. Required proportion = (7 - 5)/7 = 2/7 Detailed Solution: Let the price of the commodity be Rs. 100/kg. The price of the commodity is increased by 40%. So, the new price of the commodity = Rs. 140/kg Let us assume-we could get 'x' kg of the commodity initially for a certain amount of money and after increment in the price, we will get 'y' kg of the commodity for the same amount of money. So, x × 100 = y × 140 ⇒ y/x = 5/7 So, we can see that for the same amount of money, we will get 2 kg less after an increment in the price, while previously we used to get 7 kg. ∴ The required fraction to which the consumption must be reduced so as to maintain the same expenditure on its consumption = 2/7.