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 –

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 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%]

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 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 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.

Read concepts and formulas for: Ratio, Proportion & Variation

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