Quant (Concepts): Price and Consumption

Quant (Concepts): Price and Consumption

This article seeks to make you familiar with price and consumption, which is a very important concept related to Percentage and Profit & Loss based questions.

Say, you have Rs.100 and you want to buy a pen worth Rs. 20. Thus, you can buy 100/20 = 5 pens. If the price increases to Rs. 25 per pen, then the number of pens that can be purchased is 100/25 = 4.

Thus, increasing the price will decrease the consumption or the buying power of the customer. The quantity that is constant in this case is the money that you have or the expenditure you want to make on this item.Thus, it can be understood that, an increase in the price will reduce the quantity to be bought, and a decrease in the price will increase the quantity to be bought, provided the expenditure remains constant.

If the price of a commodity increases by X%, then the reduction in consumption, so as not to increase the expenditure will be-
= [X/ (100+X)×100]%.

If the price of a commodity decreases by Y%, then the increase in consumption, so as not to decrease the expenditure will be- 
= [Y/(100−Y)×100]%.

Example 1: The cost of petrol increases by 25%.By what percent a person should reduce his consumption considering he wants to have the same expenditure?

Sol: Increase in price = 25%.Using the formula, decrease in consumption should be-
= [25/ (100+25)×100] % = 20%.

Example 2: The consumption of wheat for a house increases by 25%.A housewife intends to buy cheaper wheat to keep expenditure constant. Earlier the price of the wheat was Rs.120. What should be the new price at which she should buy wheat?

Sol: Increase in consumption = 25%. Using the formula, decrease in price should be-
= [25/ (100-25)×100] % = 100/3% = 33.33% or 1/3.
Hence, the required price = 120-(120 × 1/3) = Rs. 80.

Further, there can be questions in which the expenditure is also changing along with either price or consumption. The following example illustrates such a problem.

Example 3: The price of rice increases by 50%. By what percent the consumption should be reduced, so that there is only 20% increase in the expenditure?

Sol: Let the initial cost of 1 kg be X
Cost after increase = 1.50 × (50% increase)

Let the initial consumption be ‘N’ kg.
Initial spent = XN.
Since increase in price = 20%, the new spent = 1.20 × N (20% increase)

Let the new consumption be 'M' kg.
Now 1.50XM = 1.20XN
⇒1.50M = 1.20N, M = 0.8N. That means M is 80% of N i.e. the new consumption is 80% of earlier consumption; therefore the consumption is reduced by 20%.