Introduction:-
Profit and Loss is an important role in competitive exams. There are questions based on profit & loss topics in almost all the competitive exams.
Here are some important statements and definitions related to profit and loss concepts.
Cost Price (CP):
The price at which goods are bought is called the cost price.
Selling Price (SP):
The price at which goods are sold is called the selling price.
Profit:
When the selling price is more than the cost price, the trader makes a profit that is equal to (SP - CP).
Loss:
When the selling price is less than the cost price, the trader makes a loss equal to (CP - SP).
Profit Percentage:
The value of profit, when expressed as a percent of the cost price (CP), is called profit percent. so, Profit percent = \(\frac{(SP-CP)}{CP} \times 100\) .
Loss Percentage:
Loss, when expressed as a percentage of cost price, is called loss percentage. So, Loss percentage = \(\frac{(CP-SP)}{CP} \times 100\).
Marked price:
Marked price is the price that is marked on the product.
Discount:
If the seller can decide to give discounts to the buyer and that case selling price might be different from the marked price.
So, Discount = (Marked price) - (Selling price).
Then discount percentage = \(\frac{Discount}{Marked \ price}\times100\).
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Some Important Formula and Tricks:-
A). Selling price calculation
1).If there is a profit of P %, and Cost Price = C (given).
Then selling price (SP) = \(\frac{(100+P)}{100}\times C \).
2). If there is a loss of L %, and Cost Price = C (given).
Then selling price (SP) =\(\frac{(100-L)}{100}\times C \).
B). Cost price calculation
1). If there is a profit of P %, And Sale price= SP (given).
Then cost price (C ) = \(\frac{100}{(100+P)}\times SP \).
2). If there is a loss of L %,
Then cost price (C) = \(\frac{100}{(100-L)}\times SP \).
C). If the price of an item increases by r% , then the reduction in consumption so that expenditure remains the same ,is
\(\frac{r}{100+r} \times 100\%\).
D). If the price of an item decreases by r% then increase in consumption , so
expenditure on this item is same, is
\(\frac{r}{100-r} \times 100\%\).
E). A reduction of x% in price enables a person to buy y kg more for Rs. A. Then the original price = \(\frac{x}{(100-x)\times y} \times A \).
And the reduction price = \(\frac{x}{100y} \times A \).
F). When there are two successive profits of x% and y% then the net profit percentage =\([x+y+\frac{xy}{100}]\).
G). When there is a profit of x% and loss of y% then net profit or loss percentage
= \([x – y – \frac{xy}{100}]\).
If negative sign occurs then loss comes, and if positive sign occurs then profit comes.
H). If A sells goods to B at a profit of x% and B sells it to C at a profit of y%. If C pays Rs P for it,then the cost price for A is
\(\frac{100\times 100\times P}{(100+x)(100+y)}\).
I). If A sells goods to B at a loss of x% and B sells it to C at a loss of y%. If C pays Rs P for it,then the cost price for A is
\(\frac{100\times 100\times P}{(100-x)(100-y)}\).
J). When each of the two things is sold at the same price,and a profit of p% is made on the first and a loss of L% is made on the second,then the percentage gain or loss is
= \(\frac{100(P-L)-2PL}{(100+P)+(100-L)}\).
Note:- If profit percentage and loss percentage are equal, put P=L
Then, loss percentage= \(\frac{P^2}{100}\).
Example:-
1. A man buys a fan for Rs. 1000 and sells it at a loss of 15%. What is the selling price of the fan?
2. If a pen cost Rs.50 after 10% discount, then what is the actual price or marked price (MP) of the pen?
3. A dishonest dealer sells goods at a 10% loss on cost price but uses 20% less weight. Compute profit or loss percentage.
4. If selling price is doubled, the profit triples. Find the profit percent.
5. A man buys a fan for Rs. 1000 and sells it at a loss of 15%. What is the selling price of the fan?
6. If a pen cost Rs.50 after 10% discount, then what is the actual price or marked price of the pen?
7. A person buys a horse for 15 pounds. After one year, he sells it for 20 pounds. After one year, again he buys the same horse at 30 pounds and sells it for 40 pounds. What is the overall profit percent for that person over both the transactions?
8. A trader sells 85 m of cloth for Rs. 8,925 at the profit of Rs. 15/m of cloth. What is the cost price of 1 m of cloth?
9. The marked price of a shirt is Rs.1000. A shopkeeper offers 30% discount on this shirt and then again offers a 20% discount on the new price. How much will you have to pay, finally?
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