# CAT Quant: Profit and Loss – Important Formulas and Concepts

## Basic Formulas

- The Selling Price (SP) and Cost Price (CP)of an article determines the profit or loss made on the particular transaction. Some basic formulas are as follows –

$$\large PROFIT$$ | $$\large LOSS $$ |

$$Profit = SP – CP $$ | $$Loss = CP – SP$$ |

$$Profit\% = \frac{Profit}{CP} *100$$ | $$Loss\% = \frac{Loss}{CP} *100$$ |

$$SP = CP{\LARGE[}1+\frac{P\%}{100}{\LARGE]}$$ | $$SP = CP{\LARGE[}1-\frac{L\%}{100}{\LARGE]}$$ |

$$CP = SP{\LARGE[}\frac{100}{100+P\%}{\LARGE]}$$ | $$CP = SP{\LARGE[}\frac{100}{100-L\%}{\LARGE]}$$ |

###### NOTE –

- When two articles are sold at the same price (i.e their SP is the same) such that there is a Profit of P% on one article and a Loss of L% on the other (i.e common Profit% and Loss% being equal) then, irrespective of what the CP actually is, the net resultant of the transaction is LOSS. Thus, it is calculated as – $$Loss\% = \frac{[Common \ P\% \ and \ L\%]^2}{100} =\frac{L^2}{100} = {\LARGE[}\frac{L}{10}{\LARGE]}^2$$
- Profit calculation on the basis of Amount Spent and Amount Earned – Profit can also be calculated without taking into account their SP or CP. One such method is- $$Profit\% = \frac{Goods Left}{Goods Sold}*100 $$
**Example**– A Seller recovers the cost of 25 shoes by selling 20 shoes. Calculate the profit percentage. $$Profit\% = \frac{Goods Left}{Goods Sold}*100= \frac{(25-20)}{20}*100=25\%$$

## Multiplying Factor [M.F]

- Multiplying Factor formulas are easily applicable in Profit and Loss. Their usage is illustrated below- $$MF=\frac{100+P\%}{100} \\ SP = CP * MF$$
- here, when calculating MF, for profit(P) – [100 + P%] and for loss(L) – [100 – L%]

## Calculating Profit/Loss directly from SP

- There is a simpler unitary method for directly calculating Profit/Loss from SP and CP given $$\frac{1}{x} \ of \ Smaller \ Quantity = \frac{1}{x+1} \ of \ Greater \ Quantity $$
- For Profit – SP (greater quantity) and CP (smaller quantity)
- For Loss – CP (greater quantity) and SP (smaller quantity)

## Break – Even Point

- Break Even Point is defined as the volume of sales at which there is no profit and no loss.
**Profit –**(Actual Sales – Break Even Sales) * Contribution per Unit**Loss –**(Break Even Sales – Actual Sales) * Contribution per Unit- Note – If Break Even Sales equals the Actual Sales, then we reach a point of no profit and no loss, which is also the functional definition of Break Even Point.

## Marked Price / List Price

- Marked Price is the price that is indicated or marked on the product. $$Markup = MP – CP \\ Markup\% = \frac{(MP – CP)}{CP} * 100$$
**CP + Markup = Marked Price [MP]****CP + Markup% on CP = Marked Price**- If product is normally sold at Market Price then,
**SP = MP** - If product is sold at a Discounted Price on the Marked Price the,
**SP = MP – Discount%**

## Discount

- When an article is sold at a price less then the Marked Price, then the amount by which the price is reduced is referred to as Discount. $$Discount = MP – SP \\ Discount\% = \frac{Discount}{MP}*100$$
**Successive Discount% –**If successive discounts are p%, q%, r% and so, on a product then the effective price after all these discounts is – $$SP = MP{\LARGE[}\frac{(100-p)(100-q)(100-r)}{(100)^3}{\LARGE]}$$**Successive Change –**When there are successive %changes, then another approach is as follows –- 1st Change (a%) and 2nd Change (b%) —
**Overall %Change = (a + b + ab/100)** - In case there are 3 %Changes namely a%, b% and c%, we take the Overall %Change of a% and b% to arrive at k% and then take the Overall % Change of k% and c% to arrive at the net resultant.

- 1st Change (a%) and 2nd Change (b%) —