Profit and Loss for the Assam Police Constable Exam
Profit and loss is the chapter that the Assam Police Constable (AB & UB) paper uses to test whether a candidate can apply percentage to a real transaction. Almost every question describes a shopkeeper, a trader or a dealer who buys an article at one price and sells it at another, and asks for the gain, the loss or the percentage of either. The arithmetic is never heavy, but the chapter is full of traps, because the base on which a percentage is measured changes with the wording of the question. A candidate who remembers one golden rule will avoid almost all of these traps: profit and loss are always calculated on the cost price, while discount is always calculated on the marked price. If this rule is kept in view, the chapter becomes one of the most dependable sources of marks in the paper. The method followed here is the one from the Master Book: Maths Masti (D. Hurina), which first writes the cost price as the base of one hundred and then expresses every other price as a percentage of it.
Why Profit and Loss Is a Favourite in the Assam Police Paper
The topic is popular with examiners because it combines three separate ideas in one place: percentage, ratio and a small amount of reasoning about what a question really asks. It also produces numerical answers that can be checked quickly, so the examiner can set neat options. For a candidate, the same three ideas make the chapter quick to master, and the questions are usually one or two lines of calculation once the correct base is fixed.
Terms You Should Know
- Cost price: the price at which an article is bought, including any overheads.
- Selling price: the price at which an article is sold.
- Marked price: the price printed on the article, also called the list price.
- Profit or gain: selling price minus cost price, when the selling price is larger.
- Loss: cost price minus selling price, when the cost price is larger.
- Discount: the reduction allowed on the marked price.
- Overhead: extra expenses such as transport, which are added to the cost price.
Whenever overheads are mentioned, they must be added to the cost price before any profit or loss is worked out, because the trader has truly spent that money.
The Four Prices and the Four Formulas
Profit equals selling price minus cost price, and loss equals cost price minus selling price. Profit percentage equals profit divided by cost price, multiplied by one hundred, and loss percentage equals loss divided by cost price, multiplied by one hundred. From these, the selling price can be written as the cost price multiplied by one plus the profit percentage, or one minus the loss percentage. Writing the selling price as a multiple of the cost price in this way is the fastest route through most questions, because it avoids the separate steps of finding the profit and then dividing.
Profit and Loss as a Percentage of Cost Price
Because the base is the cost price, a trader who sells an article for one hundred and twenty rupees after buying it for one hundred rupees has made a profit of twenty rupees, which is twenty per cent. The same twenty rupees described as a percentage of the selling price would be a different figure, and that is precisely the error the examiner hopes to catch. To find the cost price from the selling price and the profit percentage, divide the selling price by one plus the profit percentage, taking the percentage as a decimal.
Marked Price, Discount and Successive Discounts
Discount is the amount by which the marked price is reduced, and the discount percentage is always measured on the marked price. A single discount of twenty per cent is not the same as two successive discounts of ten per cent each, because the second ten per cent is taken on the already reduced price. This pair of successive discounts is equivalent to a single discount of nineteen per cent, which is less than twenty. The equivalence of two successive discounts is found by using the same multiplying-factor method that applies to any successive percentage change.
When Two Articles Are Sold at the Same Price
A classic question sells two articles at the same selling price, one at a profit of a given percentage and the other at a loss of the same percentage, and asks for the overall result. The answer is always a loss, because the article sold at a profit had a smaller cost price and the article sold at a loss had a larger cost price, so the loss is measured on the larger base. The loss percentage in this case is equal to the square of the common percentage divided by one hundred. A candidate who remembers this standard result can answer the question in a single line.
The Dishonest Dealer and the Faulty Weight
When a dealer uses a weight that is lighter than it claims, the profit percentage is found by comparing the false weight with the true weight. If a dealer uses a weight of nine hundred grams in place of one kilogram, the profit percentage is one hundred divided by nine hundred, multiplied by one hundred, which is eleven and one ninth per cent, not ten per cent, because the base is the weight the dealer actually gives. Questions on selling at cost price but using false weights are common and are solved with the same comparison.
Relation with Percentage, Ratio and Interest
Profit and loss is simply percentage applied to money, so the shortcuts of the percentage chapter carry over directly. The ratio of cost price to selling price can be written at once from the profit percentage, which often shortens a partnership or mixture question. The same reasoning also appears in simple and compound interest, where the rate is a percentage of the principal, and in questions on commission, where the commission is a percentage of the sale.
Shortcut Techniques for the Exam Hall
Take the cost price as one hundred and express every other price as a percentage of it; the profit or loss then reads off immediately. When a discount and a profit are both given, work forward from the marked price through the discount to the selling price and then to the cost price. For two articles sold at the same price, use the standard result that the outcome is a loss whose percentage is the square of the common percentage divided by one hundred. For false weights, compare the weight given with the weight claimed and treat the ratio as the profit.
Common Traps and Errors
- Calculating profit or loss on the selling price instead of the cost price.
- Calculating discount on the cost price instead of the marked price.
- Adding successive discounts instead of multiplying their factors.
- Forgetting to include overhead expenses in the cost price.
- Assuming that equal percentages of profit and loss on two equal selling prices cancel out.
- Treating a false weight of nine hundred grams as a profit of ten per cent.
A Study Plan for This Chapter
- Learn the four formulas and the meaning of the four prices.
- Practise taking the cost price as one hundred and expressing the rest as percentages.
- Work through marked price, single discount and successive discounts.
- Practise two-article and false-weight questions until the standard results are automatic.
- Finish with a mixed set that also touches interest and commission.
Frequently Asked Questions
On which price is profit percentage calculated?
Profit percentage is always calculated on the cost price, the amount the trader actually paid. This is the single most important base in the whole chapter.
Why are two successive ten per cent discounts less than twenty per cent?
Because the second discount is taken on the price that is already reduced. The two factors are zero point nine and zero point nine, whose product is zero point eight one, which means a single discount of nineteen per cent.
Why is there always a loss when two articles are sold at the same price at equal percentages of profit and loss?
Because the article sold at a profit was cheaper, so the profit is measured on a small base, while the article sold at a loss was costlier, so the loss is measured on a large base. The loss therefore outweighs the profit, and its percentage equals the square of the common percentage divided by one hundred.
How is profit found when a dealer uses a false weight?
Compare the weight actually given with the weight claimed, and take the excess as a fraction of the weight that was actually given. Using nine hundred grams in place of one kilogram gives a profit of one hundred over nine hundred, which is eleven and one ninth per cent.
Are overhead expenses part of the cost price?
Yes. Transport, repairs and similar expenses are added to the cost price before profit or loss is calculated, because the trader has genuinely spent that money.