 # Profit & Loss: Formulas & Rules

As the profit and loss questions are very common and integral part of competitive exams, you can remember the following profit loss formula to solve problems on profit and loss. Each profit and loss formula explained below will help in solving questions on the same.
• Equal % profit & loss on the same selling price of 2 articles:
If two items are sold at Rs X each, one at a loss of p % and the other at a gain of p %, then the two transactions have resulted in an overall loss of (p2/100) %. This is the loss in percentage.
The absolute value of the loss = Rs (2.p2.X)/(1002-p2)
• Equal % profit & loss on the same cost price of 2 articles:
If the cost price of two items are X, and one is sold at a loss of p % and the other at a profit of p %, then the two transactions have resulted in no loss or no gain.
It is a common practice to announce a discount on the marked price of an article so as to attract customers.
Note: The discount is always taken as % of the marked price unless otherwise specified. E.g. suppose the list price of an article is Rs. 450. A discount of 5 % on its list price is announced. Therefore, the new selling price = 450 – 5% of 450 i.e. 450 – 22.5 = Rs 427.5.
• Cash Discount:
In addition to trade discount, the manufacturer may offer an additional discount called the Cash Discount if the buyer makes full payment within a certain specified time.
Cash Discount is usually offered on the net price (the price after subtracting trade discount from the marked price). So, Cash Price = Net Price - Cash Discount
Note: The cash discount is always calculated on net price, unless otherwise specified.
• Wrong Weight: When a trader professes to sell at the cost price, but uses a false weight, then the percentage profit earned = 100×Error/True Weight-Error
• Successive Discounts: When a tradesman offers more than one discount to the customer, then sometimes you are required to calculate the single discount, which is equivalent to the two discounts given. There you can apply the method of decimals learned in the concepts of percentages. The successive discounts are a part of our daily lives as well as basic profit and loss mathematics.
E.g. a tradesman offers two successive discounts of 20% & 10%. Which single discount is equal to these two successive discounts?
Here you can assume the marked price to be 100. A discount of 20% will leave 100 – 20 = Rs. 80 behind. Now after that there is a further discount of 10%, a discount of 10% on Rs. 80 will leave 80 – 8 = Rs. 72 behind. Now for a Rs. 100 product the final price paid is Rs. 72. The total discount is 100 – 72 = 28. As the base or the marked price is Rs. 100 only, the discount percentage is 100 × 28/100 = 28%. Here this 28% is the single discount equivalent to two successive discounts of 20% and 10%. You can apply the following percentage formula to find the single equivalent discount as well.
• Single discount, which is equal to two successive discounts of m % and n % = M + N + MN/100.
But do remember in this case to take the values of discounts as negative as this formula is for change is values, which could be positive or negative. As discount is something, which will always reduce the marked price, its value should always be taken in negative only. Let us solve the above mentioned example with the help of this formula. This formula for profit and loss is very important.
M + N + MN/100 ⇒ (-20) + (-10) + (-20)(-10)/100 ⇒ -20 – 10 + 2 = - 28. Hence the single equivalent discount is 28%.
• When the SP of x articles is equal to CP of y articles, what is the earned profit in percentage?
Profit percent = 100× difference in x and y/x