Important facts that you should memorize
Cost Price : The price at which any article is purchased is called its cost price, abbreviated as C.P.
Selling Price : The price, at which an article is sold, is called its selling prices, abbreviated as S.P.
Profit : If Selling Price is greater than Cost Price then seller makes profit.
Profit = SP – CP
Loss : If Cost Price is greater than Selling Price then seller incurs loss.
Loss = CP – SP
- If an article is sold at a gain of 50%, than it means then S.P. = 150% of C.P.
- If an article is sold at a loss of 40% then S.P. = 60% of C.P.
Important Formulae of Profit and Loss
Gain Percentage (Gain %)
Loss Percentage (Loss %)
Selling Price (S.P.) in case of loss %
Selling Price (S.P.) in case of gain %
Cost Price (C.P.) in case of gain %
Cost Price (C.P.) in case of loss %
Quicker approach for tricky problems/Shortcuts
Rule 1: When a person sells two similar items, one at a gain of say x%, and the other at a loss of x% than theloss incurred by the seller is given by
Loss % =
Rule 2 : If a trader professes to sell his goods at cost price, but uses false weights, then :
Gain % =
Rule 3 : If there are two successive profits of R1% and R2% then total profit % =
Rule 4 : If there is a profit of R1% and loss of R2% then total profit or loss % =
Rule 5 : If the cost price of P article is equal to selling price of Q article where P>Q, then profit % :
Rule 6 : If a person marks his article P% above it’s cost price and gives customers a discount of Q% then net profit of loss % is :
Solved examples on Profit and Loss
Q1. A motorbike vendor recovers the cost of 25 bikes by selling 20 bikes. Find the % profit
(a) 20 % (b) 25 % (c) 15 % (d) 16 %
Here in this case price of quantity soled and Cost price are equal, so
Q2. Jethalal bought a Nokia mobile phone @ Rs. 800. He sold it to Master Bhide after allowing a discount of 10%. In this deal, Jethalal made a profit of 12.5%. What was the marked price?
- Rs. 1,000
- Rs. 1,100
- Rs. 1,200
- Rs. 1,300
Profit is always calculated on actual investment (cost price).
Cost Price: Rs.800
The question says, profit =12.5%. What is the profit in rupee terms?
|=12.5% x 800|
=(125/10)x (1/100) x 800
|12.5% =1/8 (percentage to fraction conversion table).|
So, 12.5% x800
= (1/8) x 800= Rs. 100
Anyways in either method, profit is Rs.100…Fact (i)
Jethalal gave 10% discount on marked price. So customer Bhide Master had to pay only
90% of the Marked Price.
=0.9 times the marked price
=this is the money Jethalal received from customer.
Jethalal’s actual profit
=the money he received from customer MINUS his original investment.
=0.9 times Marked price MINUS Rs.800
But recall fact (i), Jethalal’s profit is Rs.100
100=0.9 times Marked price – Rs.800
100+800=0.9 times marked price
900=0.9 x MP
MP=900 x 10/9
Final Answer: marked price is Rs.1000
In the exam hall, directly frame the equation: 0.125 x800 =(0.9 xMP)-800
Q3. A man buys an article for Rs. 27.50 and sells it for Rs 28.60. Find his gain percent
Answer: Option D
So we have C.P. = 27.50
S.P. = 28.60
Gain = 28.60 – 27.50 = Rs. 1.10
Q4. If the cost price is 25% of selling price. Then what is the profit percent.
Answer: Option C
Let the S.P = 100
then C.P. = 25
Profit = 75
Profit% = 75/25 * 100 = 300
The question given below is a sample practice problem in Profits, Discounts and Markup. It is an Arithmetic Topic and the problem provides an understanding of the core concept related to profits and discounts.
Q5. A merchant marks his goods in such a way that the profit on sale of 50 articles is equal to the selling price of 25 articles. What is his profit margin?
Correct Answer – 100% profit. Choice (3)
Answer with Explanation
Let the selling price per article be = Re. 1
Therefore, selling price of 50 articles = Rs.50
Profit on sale of 50 articles = selling price of 25 articles = Rs.25.
S.P = 50. Profit = 25. Therefore, CP = 50 – 25 = 25.
Correct answer choice (3)