Profit and Loss
Profit and loss turns the shopkeeper's everyday arithmetic into examination questions, and in ADRE Grade IV it is a dependable scoring chapter. The whole chapter rests on two prices, the cost price at which an article is bought and the selling price at which it is sold. When the selling price is greater than the cost price there is a profit, and when it is smaller there is a loss, and both are almost always expressed as a percentage of the cost price. The method followed in the Master Book: Maths Masti (D. Hurina) is to write the cost price as one hundred wherever possible, which reduces many questions to simple number work. Discount is a separate idea and is taken on the marked price, not on the cost price. Once these terms and their connections are clear, the chapter becomes a matter of careful substitution.
Basic Terms
- Cost price (CP): the price at which an article is bought.
- Selling price (SP): the price at which an article is sold.
- Profit or gain: the excess of the selling price over the cost price.
- Loss: the excess of the cost price over the selling price.
- Marked price (MP): the price written on the article, also called the list price.
- Discount: the reduction allowed on the marked price.
- Overhead: extra expenses such as transport or repair added to the cost price.
Main Formulas
- Profit equals selling price minus cost price.
- Loss equals cost price minus selling price.
- Profit per cent equals profit divided by cost price, multiplied by one hundred.
- Loss per cent equals loss divided by cost price, multiplied by one hundred.
- Selling price equals cost price multiplied by one hundred plus profit per cent, divided by one hundred.
- Cost price equals selling price multiplied by one hundred, divided by one hundred plus profit per cent.
Profit and loss per cent are always taken on the cost price, while discount is always taken on the marked price. Keeping this distinction in mind removes most of the confusion between the two ideas.
Equal Selling Price and the Standard Result
If two articles are sold at the same selling price, one at a profit of x per cent and the other at a loss of x per cent, there is always a net loss, and the loss per cent is x multiplied by x divided by one hundred. For example, two articles sold at the same price with a ten per cent profit and a ten per cent loss produce a net loss of one per cent. The reason is that the profit is calculated on the smaller cost price and the loss on the larger one, so the loss always outweighs the profit.
Marked Price and Discount
Discount is the amount by which the marked price is reduced to arrive at the selling price, and the discount per cent is calculated on the marked price. The selling price is therefore the marked price multiplied by one hundred minus the discount per cent, divided by one hundred. Questions often give the discount and ask for the profit or loss, and the safe route is to find the selling price from the marked price first and then compare it with the cost price.
Successive Discounts
When two discounts are allowed one after the other, they are not added. If the discounts are a per cent and b per cent, the single equivalent discount is a plus b minus their product divided by one hundred. Two successive discounts of ten per cent each are therefore equal to a single discount of nineteen per cent, and not twenty per cent. This result is the same successive-change formula met in the chapter on percentage, and it is a common source of error when it is ignored.
Dishonest Dealer and False Weight
A dealer who uses a false weight while claiming to sell a full quantity earns a profit even when he sells at the cost price. If goods worth one thousand grams are actually given as nine hundred grams, the gain per cent is the error divided by the quantity actually given, multiplied by one hundred, which is eleven and one ninth per cent. Such questions test whether the candidate understands that profit depends on the real cost of what is given.
Relation with Percentage and Ratio
The profit and loss chapter rests firmly on percentage and ratio. Writing the cost price as one hundred lets the profit per cent be read off directly, and a profit per cent is converted into the ratio of selling price to cost price by adding the profit per cent to one hundred and writing it over one hundred. Similarly, when the ratio of selling price to cost price is known, the profit or loss per cent follows at once. Once these connections are clear, many questions can be done mentally, which saves valuable time in the examination.
How This Chapter Appears in the Examination
Profit and loss questions in ADRE Grade IV, APSC and Assam Police papers usually ask the candidate to find the profit or loss per cent, to find the selling price from the cost price and the profit per cent, to find the cost price from the selling price, to work out a discount on a marked price, or to handle a successive discount. The chapter is closely tied to percentage and to ratio, and a good grasp of the cost price as one hundred removes most of the calculation. Because the situations are familiar and the formulas are few, this is a strong scoring section.
Shortcut Methods for Rapid Calculation
Assume the cost price to be one hundred whenever no actual price is given, since all the percentages are then read off directly. To convert a profit per cent into the ratio of selling price to cost price, add the profit per cent to one hundred and write it over one hundred. In successive discount questions use the single equivalent discount formula. These tricks keep the arithmetic in whole numbers and save time in the examination.
Common Mistakes to Avoid
- Calculating profit per cent on the selling price instead of the cost price.
- Calculating discount on the cost price instead of the marked price.
- Adding two successive discounts instead of using the equivalent discount.
- Forgetting to add overhead expenses to the cost price.
- Assuming that equal profit and loss per cents on the same selling price cancel out.
How to Prepare This Topic
- Learn the meanings of cost price, selling price, marked price and discount.
- Memorise the main formulas and practise each in both directions.
- Use the cost price as one hundred method for percentage questions.
- Work on discount and successive discount problems.
- Finish with mixed sets on false weight and equal selling price.
Frequently Asked Questions
Profit per cent is taken on which price?
Profit per cent and loss per cent are always taken on the cost price, because that is the money the seller has actually invested. Discount, on the other hand, is always taken on the marked price.
Why do equal profit and loss per cents on the same selling price give a loss?
Because the profit is calculated on the smaller cost price and the loss on the larger one. The loss therefore outweighs the profit, and the net loss per cent is x squared divided by one hundred.
What is the difference between marked price and selling price?
The marked price is the price written on the article. The selling price is what the buyer actually pays after the discount has been allowed on the marked price.
How do I find cost price when selling price and profit per cent are known?
Multiply the selling price by one hundred and divide by one hundred plus the profit per cent. For a loss, subtract the loss per cent from one hundred in the denominator.
Do two discounts of ten per cent equal a discount of twenty per cent?
No. Two successive discounts of ten per cent give a single equivalent discount of nineteen per cent, because the second discount is taken on the already reduced price.