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**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**

**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**

**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 %

**Solution:**

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

**Solution**

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?

Long cut | Shortcut |

=12.5% x 800 =(125/10)x (1/100) x 800 =Rs. 100 | 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

Therefore

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

MP=Rs. 1000.

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

- 1%
- 2%
- 3%
- 4%

**Answer:** Option **D**

**Explanation:**

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.

- 150%
- 200%
- 300%
- 350%

**Answer:** Option **C**

**Explanation:**

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?

- 25%
- 50%
- 100%
- 66.67%

**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)