## Profit and Loss

**Important Terms:**

**Cost Price (C.P.):**Price at which at an article is purchased.

**Selling Price (S.P.):**Price at which at an article is sold

**Profit/Gain:**The seller is said to be in profit, if selling price (S.P.) is greater than cost price (C.P.)

**Loss:**The seller is said to be in loss, if selling price (S.P.) is lesser than cost price (C.P.)

**Important Formulae:**

1) Loss% = | Loss | × 100 |

C.P. |

2) Profit% = | Profit | × 100 |

C.P. |

**3) When shopkeeper earns profit,**

Cost Price = | 100 | × S.P. - - - - - - (Given: Gain% and selling price of an article) |

(100 + Gain%) |

Selling Price = | (100 + Gain%) | × C.P. - - - - - - (Given: Gain% and cost price of an article) |

100 |

**4) When shopkeeper incurs loss,**

Cost Price = | 100 | × S.P. - - - - - - (Given: Loss% and selling price of an article) |

(100 - Loss%) |

Selling Price = | (100 - Loss%) | × C.P. - - - - - - (Given: Loss% and cost price of an article) |

100 |

**Quick Tips and Tricks**

**1) Profit =**(S.P.) > (C.P.)

**2) Loss =**(S.P.) < (C.P.)

**3)**If profit earned by selling an article is 25 %, then S.P. = 125% of C.P.

**4)**If an article is sold at a loss of 30 %, then S.P. = 70 % of C.P.

**5)**A shopkeeper sells two similar items A and B. If A is sold at a gain of x % and B is sold at a loss of x %, then shopkeeper always incurs a loss given by:

Loss% = | Common loss and gain% | ^{2} | = | x | ^{2} | ||||

10 | 10 |

**6)**A trader sells goods at cost price but uses a weight of x kg instead of y kg (false weights) and makes profit. This profit can be calculated using the formula shown below:

True weight – False weight = Error

Gain% = | Error | × 100 | % | ||

(True weight – Error) |

**7)**If cost price of X articles is equal to selling price of Y articles, then profit can be calculated using the formula:

**a) C.P. of X = S.P. of Y**

**b) Number of X articles > Number of Y articles**

Profit% = | No. of X articles – No. of Y articles | × 100 |

No. of Y articles |

**8)**If a seller makes X % above C.P. and offers a discount of Y%, then profit % or loss % can be calculated using the formula:

Profit or Loss% = (X – Y) – | X × Y |

100 |

**9) Discount:**

a) Discount% = | Discount | × 100 |

Marked Price (M.P.) |

b) If D1, D2, D3 are percentage of successive discounts on M.P., then S.P. | = | Marked Price | 1 – | D1 | 1 – | D2 | 1 – | D3 | ||||||

100 | 100 | 100 |

Single equivalent discount percentage = | (a + b) – | ab | ||

100 |

**Question Variety**

Type 1: To find Profit/Loss or Selling Price/Cost Price.

**Q 1.**A shopkeeper sells an article for Rs. 200 with a loss of Rs. 20 %. Find the cost price of the article.

a. 220

b. 250

c. 280

d. 260

View solution

Correct Option: (b)**Hint: **

Cost Price = | 100 | × S.P. |

(100 – Loss%) |

S.P. = Rs. 200 and loss = 20

Cost Price = | 100 | × 200 |

(100 – 20) |

Cost Price = | 100 | × 200 |

80 |

**Q 2.**A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit?

a. 75.65

b. 73.26

c. 72.50

d. 70.78

View solution

Correct Option: (a)

We are given selling price = Rs. 580 and expected profit of 15 %

Therefore, we can easily solve this numerical, considering basic formulae of profit and loss.

Let cost price = x

Selling price = C.P. + Profit

S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price)

580 = x + (0.15 x)

580 = 1.15 x

Therefore,

x = 504.347

Cost Price = Rs. 504.35

Now, we have the cost price and hence,

Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65

The trader gets a profit of Rs. 75.65**Alternate solution: ** This numerical can be easily solved using the trick specified below. Using such tricks reduce time consumed to solve the numerical.**Hint: **

Cost Price = | 100 | × S.P. |

(100 + Gain%) |

Cost Price = | 100 | × 580 |

(100 + 15) |

Cost Price = | 100 | × 580 = Rs. 504.35 |

(115) |

Therefore,

Profit = C.P. – S.P.

C.P. = Rs.504. 35 and S.P. = Rs. 580

Profit = 580 – 504.35 = Rs. 75.65

The trader gets a profit of Rs. 75.65

**Q 3.**If a boy sells a book for Rs. 450 he gets a loss of 10 %, then find cost price. To gain 10 %, what should be the selling price?

a. 400, 500

b. 550, 600

c. 500, 550

d. 475, 525

View solution

Correct Option: (c)**1) Find cost price**

Let C.P. of book = x and S.P. = Rs. 450

S.P. of book = C.P. – (10% of C.P.)

S.P. = x – (0.10x)

450 = 0.9 x

x i.e cost price = Rs. 500**2) Find Selling Price to gain 10 %.**

Now, we are asked to find selling price to gain 10% profit.**Hint: **

Selling Price = | (100 + Gain%) | × C.P. |

100 |

Selling Price = | (100 + 10) | × 500 |

100 |

Selling Price = | (110) | × 500 |

100 |

Therefore, selling Price = Rs. 550

**Q 4.**A merchant sells 30 metres of cloth and gains selling price of 10 metres. Find the gain percent.

a. 15 %

b. 25 %

c. 50 %

d. 75%

View solution

Correct Option: (c)

Here, selling price of 10 m cloth is obtained as profit.

Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)

Selling price of 20 m cloth = Selling Price of 30 m of cloth

Let cost of each metre be Rs. 100.

Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000

Profit% = | 10 | × 100 = 50% |

20 |

Profit of 50 % was made by the merchant.