Hello aspirants, Profit and Loss problems are found in almost all entrance exams. Let us take a look\r\nat some key concepts regarding this subject.
\r\n\r\nSome important terms and formulae for Profit and Loss problems
\r\nCost Price(C.P)
\r\nThe price at which an article is purchased is called the Cost Price of that article.
\r\n\r\nSelling Price(S.P)
\r\nThe price at which an article is sold is called the selling price of that article.
\r\nTip: In a transaction the C.P of the article can be S.P of the same article for different persons.\r\nFor 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\r\nthe selling price for person X.
\r\n\r\nGain /Loss: = S.P - C.P
\r\nIf S.P - C.P is positive then it is called Gain and if S.P - C.P is negative then it is called Loss.
\r\nWhile solving problems, we take |loss|.
\r\nPercentage Gain = $ frac{Gain}{C.P} * 100.$
\r\nPercentage Loss = $ frac{Loss}{C.P} * 100.$
\r\nIf an article is sold at a gain of 30%, then S.P = 135% of C.P
\r\nIf an article is sold at a loss of 30%, then S.P = 70% of C.P
\r\nWhen a person sells two similar items, one at gain x% and other at a loss of x% then,
\r\n seller incures loss of $ (frac{x}{10})^2 = frac{x^2}{100} $
\r\nIf a trader posses to sell his goods at C.P , but uses false weight, then
\r\n$ Gain% = frac{Error}{True Value - Error} * 100. $
\r\nLet\'s solve a unique type of problem:
\r\nPure ghee costs RS. 100 per kg. After adulterating with vegetable oil costing Rs.50 per kg, a shopkeeper sells the\r\nmixture at the rate of RS.96 per kg, thereby making a profit of RS. 20%. In what ratio, it mixes the two?
\r\nSolution:
\r\nThe shopkeeper makes profit of 20% on Rs.96, so we have to calculate the actual C.P of adulterated mixture
\r\n$ C.P = frac{100}{ (100 + Gain)} * S.P = 96 * frac{100}{120} $ = RS.80 per Kg.
\r\nNow, Suppose x quantity of pure ghee and y quantity of vegetable oil is present in mixure, then we have,
\r\n$ 100x + 50y = 80 .....(I) $
\r\n& $ x+y = 1 ................(II)$
\r\nAfter solving equations I & II, we get $ x = frac{3}{5} $ kg & $y = frac{2}{5} $ kg
\r\nRatio of x to y is 3:2.
\r\n Thank you for reading. Solve some more examples by yourself for practice. Keep visiting.