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Profit and Loss

Hello MBA aspirants, Profit and Loss problems are found in almost all MBA entrance exams. Let us take a look at some key concepts regarding this subject.

Some important terms and formulae for Profit and Loss problems

Cost Price(C.P)

The price at which an article is purchased is called the Cost Price of that article.

Selling Price(S.P)

The price at which an article is sold is called the selling price of that article.

Tip: In a transaction the C.P of the article can be S.P of the same article for different persons. For EX. If a person X sells the article for price P to person Y, then P is the C.P of the article for person Y and P is the selling price for person X.

Gain /Loss: = S.P - C.P

If S.P - C.P is positive then it is called Gain and if S.P - C.P is negative then it is called Loss.
While solving problems, we take |loss|.

Percentage Gain = $ \frac{Gain}{C.P} * 100.$

Percentage Loss = $ \frac{Loss}{C.P} * 100.$

If an article is sold at a gain of 30%, then S.P = 135% of C.P
If an article is sold at a loss of 30%, then S.P = 70% of C.P

When a person sells two similar items, one at gain x% and other at a loss of x% then,
seller incures loss of $ (\frac{x}{10})^2 = \frac{x^2}{100} $

If a trader posses to sell his goods at C.P , but uses false weight, then
$ Gain% = \frac{Error}{True Value - Error} * 100. $

Let's solve a unique type of problem:
Pure ghee costs RS. 100 per kg. After adulterating with vegetable oil costing Rs.50 per kg, a shopkeeper sells the mixture at the rate of RS.96 per kg, thereby making a profit of RS. 20%. In what ratio, it mixes the two?
The shopkeeper makes profit of 20% on Rs.96, so we have to calculate the actual C.P of adulterated mixture
$ C.P = \frac{100}{ (100 + Gain)} * S.P = 96 * \frac{100}{120} $ = RS.80 per Kg.

Now, Suppose x quantity of pure ghee and y quantity of vegetable oil is present in mixure, then we have,

$ 100x + 50y = 80 .....(I) $
& $ x+y = 1 ................(II)$

After solving equations I & II, we get $ x = \frac{3}{5} $ kg & $y = \frac{2}{5} $ kg
Ratio of x to y is 3:2.

Thank you for reading. Solve some more examples by yourself for practice. Keep visiting. HTML5 Icon

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