# Maths Tips Profit and Loss Formulas, Problems

Here we are listed All the Important terms, Formulas, Problems of Profit and Loss on General Aptitude. Those Maths Tips will help you get maximum marks from this section. This file will be updated regularly, So please bookmark this page on your browser to get latest updates. You can also download the PDF file of the following below.

Important Terms

SP – Selling price |

CP – Cost price |

MP – Marked price |

Formulas

Profit = SP – CP |

Loss = CP – SP |

Profit% = ((SP – CP)/CP) * 100 |

Loss% = ((CP – SP)/CP) * 100 |

SP = (1+ profit%) * CP |

SP = (1 – Loss%) * CP |

CP = SP/(1+profit%) |

CP = SP/(1-Loss%) |

MP = SP+ Discount |

MP = SP/(1-Disount%) |

Discount% = ((MP – SP) / MP) * 100 |

Profit% = MP% – Discount% – (MP% * discount%) |

If profit and loss are same(x), then loss%= (X/10)2 |

#### Problem:

**1)** A person incurs 5% loss by selling a watch for Rs.1140 at what price should the watch be sold is earn 5% profit?

Solution:

*CP = SP/(1-Loss%)*

*CP = 1140*100/(100-5)*

*CP = 1200*

*To incur 5% profit the product should be sold = 1200*105/100*

*SP = 1260*

**2)** An article sold at a loss of 10%, Its CP is 800. A discount of 20% was offered on the labeled price while selling. What is the loss% at the labeled price?

**Solution:**

*SP = (1- loss%)*CP*

*SP = 800*90/100 = 720*

*MP = SP/(1-Disount%)*

*MP = 720/(1-20%) = (720*100)/80 = 900*

*Loss % at labeled price = ((MP-SP)/MP)*100*

*Loss% = ((900-720)/900)*100 = 20%*

**3)** By what percent must the cost price be raised in fixing the sale price in order that there may be a profit of 20% after allowing a commission of 10%.

**Solution**:

*Usual method: CP =100 rs , profit = 20%*

*SP = 120 rs*

*Commission 10%, then MP = SP/(1-discount%)*

*MP = 120/(1-10%) = 120/(1-(10/100))*

*=120* 100/(100-10) *

*= 133.3 rs*

*MP% = ((MP- CP)/CP)*100*

*=33.3% *

So MP should be 33.3% more than CP to get 20% profit after allowing the commission of 10%

**Shortcut** :

*Profit%= MP% – Discount% – (MP%*discount%)*

*Let MP%=x%*

*20/100 = x/100 – 10/100 – ((x/100)*(10/100))*

*30/100 = 90x/10000*

*X = 33.3%*

**4)** The price of land came to a person through three middlemen each gaining 20% if the person purchased the land for RS.3,45,600 the original cost of land was?

**Solution** :

*CP = SP/(1+profit%)*

*CP = 345600*(100/120)*(100/120)*(100/120)*

*CP = 2,00,000 rs*

**5)** A cloth merchant sold half of his cloth at 20% profit and half of the remaining cloth at 20% loss and remaining at the cost price. In total transmission what will be his gain or loss?

**Solution**:

*Let CP = 100*

*Half of the cloth at 20% profit, SP = 50 *120/100 = 60*

*Half of the remaing cloth at 20% loss, SP = 25 *80/100 = 20*

*Reaming cloth at CP, Therefore SP = 25*

*On total transaction SP = 60 + 20 +25 = 105*

*Profit% = 5%*