Shortcuts in Quantitative Aptitude for Competitive Exams – Profit and Loss
The amount paid to purchase an article or the price at which an article is made, is known as its cost price. The cost price is abbreviated as C.P.
The price at which an article is sold, is known as its selling price.
The selling price is abbreviated as S.P.
If the selling price (S.P.) of an article is greater than the cost price (C.P.), then the difference between the selling price and cost price is called profit.
Thus, If S.P. > C.P.,then
Profit = S.P. – C.P.
=> S.P. = C.P. + Profit
=> C.P. = S.P. – Profit.
If the selling price (S.P.) of an article is less than the cost price (C.P.), then the difference between the cost price (C.P.) and the selling price (S.P.) is called loss.
Thus, if S.P. < C.P., then
Loss = C.P. – S.P.
=> C.P. = S.P. + Loss
=> S.P. = C.P. – Loss
Profit and Loss percentage
- The profit per cent is the profit that would be obtained for a C.P.of Rs.100.
- Similarly, the loss per cent is the loss that would be made for a C.P.of Rs.100.
- Profit =
- Loss =
- S.P. =
- S.P. =
- C.P. =
- C.P. =
- If an article is sold at a certain gain (say 45%), then SP = 145% of CP
- If an article is sold at certain loss (say 25%), then SP = 75% of CP.
Dishonest Dealing :
Real Profit/Loss Percentage :
If the profit or loss is calculated on S.P., then it is not actual profit or loss. Real profit (loss)% is the profit (loss)% on C.P.
Goods passing through successive hands
- When there are two successive profits of a% and b%, then the resultant profit per cent is given by
- When there are two successive loss of a% and b%, then the resultant loss per cent is given by
- When there is a profit of a% and loss by b% in a transaction, then the resultant profit or loss per cent is given by
, according to the +ve or -ve sign respectively.
- When cost price and selling price are reduced by the same amount (A) and profit increases then cost price (C.P.)
- If cost price of x articles is equal to the selling price of y articles, then profit/loss percentage = , according to -ve sign respectively.
- A man purchases a certain number of articles at x a rupee and the same number at y rupee. He mixes them together and sells them at z rupee. Then his gain or loss %
, according as the sign is +ve or -ve.
- If two items are sold, each at Rs. x, one at a gain of p% and the other at a loss of p%, there is an overall loss given by . The absolute value of the loss is given by
- If CP of two items is the same and % Loss and % Gain on the two items are equal, then net loss or net profit is zero.
- A businessman sells his items at a profit/loss of a%. If he had sold it for Rs.R more, he would have gained/lost b%. Then,
CP of items =
‘-’ = When both are either profit or loss
‘+’ = When one is profit and other is loss
- If A sold an article to B at a profit (loss) of r1% and B sold this article to C at a profit (loss) of r2%, then cost price of article for C is given by (cost price for A) ×
- If a man purchases m items for Rs. x and sells n items for Rs. y, then Profit or loss per cent is given by
- [Positive result means profit and negative result means loss].
- The price on the lable is called the marked price or list price.
- The marked price is abbreviated as M.P.
The reduction made on the ‘marked price’ of an article is called the discount.
When no discount is given, ‘selling price’is the same as ‘marked price
- Discount = Marked price x Rate of discount.
- S.P. = M.P. – Discount.
- Discount % =
- Buy x get y free i.e., if x + y articles are sold at cost price of x articles, then
the percentage discount =
In successive discounts, first discount is subtracted from the marked price to get net price after the first discount. Taking this price as the new marked price, the second discount is calculated and it is subtracted from it to get net price after the second discount. Continuing in this manner, we finally obtain the final selling price. In case of successive discounts a% and b%, the effective discount is
NOTE : If the list price of an item is given and discounts d1 and d2 are given succesively on it then,
To meet government’s expenditures like construction of roads, railway, hospitals, schools etc. the government imposes different types of taxes.
- Sales tax (S.T.) is one of these tax.
- Sales tax is calculated on selling price (S.P.)
If discount is given, selling price is calculated first and then sales tax is calculated on the-selling price of the article.
If ‘a’th part of some items is sold at x% loss, then required gain per cent in selling rest of the items in order that there is neither gain nor loss in whole transaction, is