### PROFIT AND LOSS math capsule

**Did you ever wondered how a shopkeeper is going to maintain his orders?**

**or how a lady is going to organise her monthly budget?**

**they all here and there use concepts of profit and loss , either knowingly or unknowingly,**

## COST PRICE :

The price, at which an article is bought is called its cost price. All the overhead in the transaction like fright, damage , etc., are added to the cost price. Profit and loss percentage is always calculated as the percentage of CP unless otherwise specified.

## SELLING PRICE :

The price at which an article is sold is called its selling price. There is a gain in the transaction, if SP>CP, where gain = SP-CP .

There is a loss in the transaction , if CP>SP, where, loss= CP-SP

## LIST PRICE / MARKED PRICE :

The price of article excluding tax is known as marked price. Sometimes the shopkeeper increases or decreases the cost price ,then this price is the list price of the articles.

### FORMULAS YOU NEED TO REMEMBER

###
- PROFIT = SELLING PRICE - COST PRICE
- LOSS = COST PRICE - SELLING PRICE
- PROFIT AND LOSS IS ALWAYS CALCULATED ON COST PRICE
- PROFIT % = (PROFIT / CP) * 100%
- LOSS % = (LOSS / CP) * 100%

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IMPORTANT RULES

- If there is a profit of r% , then SP = (100 + r)*CP / 100 and CP = (100*SP) / (100 + r)
- If there is a loss of r% , then SP = (100 - r)*CP / 100 and CP = (100*SP) / (100 - r)
- When there are two successive profits of x% and y% then the resultant profit percent is given by (x + y + (x*y / 100) ) %
- When there are two successive losses of x% and y% then the net loss per cent is given by (-x -y + (x*y / 100) ) %
- Where there is a profit of x% and loss of y% then the resultant profit or loss per cent is given by (x - y - (x*y / 100) )%
- If the cost of both the item be S. One is sold at a loss of r % and the other at a gain of R% , then Cost price of item sold at loss = (S* (100 + R)) / ((100 - r)+(100 + R)) Cost price of item sold at gain = (S* (100 - r)) / ((100 - r) + (100 + R))
- If 'a' part is sold at l% profit, 'b' part is sold at m% profit and 'c' part is sold at n% profit. If rs 'R' is earned as overall profit , then the value of total consignment = (R * 100) / (al + bm + cn)
- If a certain number of articles are purchased at 'r' a rupee and the same number at 'R' a rupee . He mixes them together and sells them at 'M' a rupee. Then, gain per cent or loss per cent =[(2Rr / M(r+R)) -1]* 100 % According as the sign +ve or -ve , If M = (r+R)/2 there is always loss. If r=R=M there is neither gain nor loss
- If cost price of 'n' articles is equal to the selling price of 'm' articles, then Profit Percentage = ((n - m) / m) * 100 % (n>m) and Loss Percentage =((m - n) /m )* 100% (m>n)

#### SELLING PRICE = MARKED PRICE - DISCOUNT

- If discount allowed is r%, then selling price = (100 - r) * marked price / 100
- If a shopkeeper marks his items at x% above the cost price and allows customers a discount of y% for cash, then there is (x - y - (xy / 100))% profit or loss according to positive or negative sign , respectively.
- Single discount equivalent to three successive discounts r1%, r2% and r3% = [1 - (1 - r1/100)*(1 - r2/100)*(1 - r3/100)] * 100%
- If marked price price of an item is rs x and the successive discount rates are r1% , r2% , r3% and so on , then selling price of item SP = x * (1 - r1/100 ) * (1 - r2/100 ) * (1 - r3/100)

**kindly attempt the exercises too :)**

PROFIT AND LOSS EXERCISE 1 |

PROFIT AND LOSS EXERCISE 2 |

PROFIT AND LOSS EXERCISE 3 |

HINTS AND SOLUTIONS 1 PROFIT AND LOSS |

HINTS AND SOLUTIONS 2 PROFIT AND LOSS |

HINTS AND SOLUTIONS 3 PROFIT AND LOSS |

HINTS AND SOLUTIONS 4 PROFIT AND LOSS |

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