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 –
$$\large PROFIT$$$$\large LOSS $$
$$Profit = SP – CP $$$$Loss = CP – SP$$
$$Profit\% = \frac{Profit}{CP} *100$$$$Loss\% = \frac{Loss}{CP} *100$$
$$SP = CP{\LARGE[}1+\frac{P\%}{100}{\LARGE]}$$$$SP = CP{\LARGE[}1-\frac{L\%}{100}{\LARGE]}$$
$$CP = SP{\LARGE[}\frac{100}{100+P\%}{\LARGE]}$$$$CP = SP{\LARGE[}\frac{100}{100-L\%}{\LARGE]}$$
  • 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%


  • 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.

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