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Syllabus for CAT examination

Number Systems and interconversion between binary,decimal & hexadecimal Systems

Tips and formulae for solvingProbability problems

Some tips for solving Time and Work problems

Some important tips and tricks for solving two body or relative motion problems

Some Tips for CAT Reading Comprehensions

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

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

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|.

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.