**Free Online Preparation for CAT 2009 with Minglebox e-CAT Prep. Cover basic concepts of Percentage, Profit and Loss under Quantitative Aptitude for MBA Entrance Exam Preparation with Study material, solved examples and tests prepared by CAT coaching experts. **

A student get 20 marks out of 30 in an examination , then we express this information as follows . If the student got 20 marks when the total marks were 30 what would he have got if the total marks was 100?

The amount to this question is = = 66.66% .

The person of finding the answer to the question what is the value if total in 100 is what leads is to percentage . This if we say student scored 66.66 percent it mean if total is 100 then student got 66.66 marks.

Equivalence between fraction and percentage

Fraction |
**Equivalence Percentage** |

1 |
100% |

1/2 |
50% |

1/3 |
33.33% |

1/4 |
25% |

1/5 |
20% |

1/6 |
16.67% |

1/7 |
14.28% |

1/8 |
12.5% |

1/9 |
11.11% |

1/11 |
9.09% |

If a quantity A is increased by 'x' then percentage increase =

= %

If a quantity is increased by a% then new value is given by similar if a quantity is decreased by a% then new

value is given by .

If a quantity is increased by a% and then further by b% these percent change given are equivalent to a single percent change given by

%

Similarly if there is a successive decrease of a% followed by b% then effective percentage decrease is

Selling Price, Marked Price and Cost Price

**Selling price**

(SP) is the price at which an article is sold cost price is the price at which an article is bought. If SP > CP then the difference SP – CP is known as the profit , P P = SP – CP

and if SP < CP then the difference CP – SP is known as loss, L L = CP – SP

Profit Percentage P% =

Loss Percentage L% =

**Marked price**.

The price which is displayed on the tag of the article is known as marked price.

Generally the SP is less then the marked price (MP) the difference MP – SP is known as discount D

Discount % , D% =

**Question**

A shopkeeper sells sugar for Rs 25 per kg and makes a profit of 20%. If he sells the sugar for Rs 22.50 per Kg find his profit ?

**Solution **

Let the cost price CP of sugar be rs x per Kg then SP = CP + Profit

But Profit =

SP =

25 = CP (1.2)

CP =

Hence profit when SP is 22.50 Rs/ Kg

= 1.67 Rs/Kg

Profit % = %

**Question**

Mango bite is available for Rs 8 a dozen . If the shopkeeper offer a discount of 10% how many mango bites can be purchased for Rs 2.4

**Solution**

Discount Percentage = 10%

Marked price for 12 mango bites = Rs 8

8P of 12 mango bites = MP – Discount

Discount =

Hence SP =

12 toffees are available for Rs 7.2 hence for 2.4 we get 4 toffees.

**Question**

A men sells 2 pens Rs 100 each at a profit of 10% and another at a loss of 10% find his overall project or loss percentage.

**Solution **

If the cost price of the 2 pens be x an y respectively then using profit % we get

CP = in case of project

and CP = in case of loss

Hence x = and y =

x = and y

Total CP of both pens =

Total loss =

=

=

Loss % =

= 1%

*Note*

In case 2 article are sold at same selling price one at a profit of a% another are at a loss of a% then there is overall loss on the whole out lay and loss percentage is given by

%

**Question**

20 is 16% of what number?

**Solution**

If number is 100 then 16% of 100 is 16 so if 20 is 16% of some number then

number =

**Question**

A company decided to reduce the price of its product by 20% . By what percentage the sales volume should increase , so that the total revenues of the company remains unchanged ?

**Solution**

Revenues(R) =

R = …............. (1)

New price =

Hence if ' ' is the new volume then

........... (2) equating (1) and (2)

We get

=

=

=

Therefore percentage increased is volume

= %

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