Quantitative Aptitude Questions: Profit and Loss

The profit of any business enterprise over a period of time is its total revenue minus total costs.

Profits can be positive or negative. Negative profits are called losses in everyday language and usually the word profit is used only if total revenue exceeds total costs.

We shall, however, not follow this convention and allow profits to be negative. A loss of five hundred rupees can be equivalently described as a profit of minus five hundred rupees. This makes for economy of expression. We do not have to make unnecessarily cumbersome statements like saying, “Given the total costs, to calculate total revenues, if there was a profit, add it to the costs and if there was a loss, subtract it from the costs”. Instead, we can simply say, “Add profits to total costs to get total revenue”.

Measuring the revenues and costs of a business is not a simple job. We shall assume away some of the difficulties by looking at profits and losses of only those businesses that do not incur any capital expenditures and that do not hold any inventories of raw materials and goods under process.

For example, consider a vendor who sells flowers on the pavement. His only cash expenditure is on buying flowers in the morning. His revenue comes from selling these flowers during the day. Any flowers not sold during the day become useless and have to be discarded. Profit rates are usually expressed as a percentage of the money invested in the business venture. In our example, the only investment is the money spent in the morning on buying flowers.

Hence, the profit for our flower seller, expressed in percentage terms will be:

If the profit rate is negative, say (-15) %, we call it a loss of 15%. If we happen to have a rather unusual flower seller who buys only one kind of flower and manages to sell all of them (each flower at the same price) before the day is over, the formula simplifies to:

If we are given the profit rate and the cost price, the above formula can be rewritten as:

If the selling price and the profit rate are given, we can use:

Example 1   
Suppose our flower seller buys roses at a price of Rs 50 per dozen and manages to sell three fourths of them at the rate of Rs 80 per dozen during the day. If he sells the remaining roses in a special “Evening Sale” at a lower promotional price of Rs 40 per dozen, What is his rate of profit?

Solution
Let the number of roses bought by the flower seller be x dozens. His total cost is 50x rupees and the total revenue is:

The profit, therefore, is 70x – 50x = 20x rupees

The rate of profit is

(Notice that the answer does not depend on x).