PERCENTAGE

Word problems on percentage play a major role quantitative aptitude test. There is no competitive exam without the questions from this topic. In GMAT, GRE, SAT and ACT syllabus also, percentage word problems are being given some considerable weight age. We have already learned this topic in our lower classes.Even though we have been already taught this topic in our lower classes, we need to learn some more short cuts which are being used to solve the problems in the above topic.

The only thing we have to do is,
we need to apply the appropriate short cut and solve the problems in a
limited time. This limited time will be one minute or less than one minute in most of
the competitive exams.

1.Percentage is the way in which we express a number in terms of fraction of 100. The word "PERCENT" is formed by the combination of the two words "PER" and "CENT". That means per hundred.For example 45% = 45/100 or 0.45 |

2.If "x" is increased by P%, the value after increment = [(100+P)/100]x and increased value = P%of x = Px/100 |

3.If "x" is decreased by P%, the value after decrement = [(100-P)/100]x and decreased value = P%of x = Px/100. |

4.If "x" is P% less than "y", then "y" is (100P/100-P)% more than "x" |

5.If "x" is P% more than "y", then "y" is (100P/100+P)% less than "x" |

6.If the price of a product is increased by P%, then the consumption will be decreased by (100P/100+P)%. So that the total expenditure remains same. |

7.If the price of a product is decreased by P%, then the consumption will be increased by (100P/100-P)%. So that the total expenditure remains same. |

Students who are preparing to improve their aptitude skills and those who are preparing for this type of competitive test must prepare this topic in order to have better score. Because, today there is no competitive exam without questions from the topic time and work problems. Whether a person is going to write placement exam to get placed or a students is going to write a competitive exam in order to get admission in university, they must be prepared to solve word problems on percentage. This is the reason for why people must study this topic.

As we mentioned in the above paragraph, a person who wants to get placed in a company and a students who wants to get admission in university for higher studies must write competitive exams like placement test and entrance exam. To meet the above requirement, it is very important to score more marks in the above mentioned competitive exams. To score more marks, they have to prepare this topic. Preparing this topic would definitely improve their marks in the above exams. Preparing this topic is not difficult task. We are just going to remember the stuff that we have already learned in our lower classes

Short cut is nothing but the easiest way to solve percentage word problems. In competitive exams, we will have very limited time to solve each problem. Then only we will be able to attend all the questions. If we do problems in competitive exams in perfect manner with all the steps, it will definitely take much time and we may not able to attend the other questions. So we need some other way in which the problems can be solved in a very short time. The way we need to solve the problem quickly is called as shortcut.

**Here, we are going to have some word problems on percentage for which you can check your answer online and see step by step solution.**

1. The production of rice increased by 50% from 1995 to 1996.By what percentage should the production of rice be increased from 1996 to 1997, so that the production of rice in 1997 becomes six times that of 1995?

Let 100 tons be the production of rice in 1995

1995 ===> 100 tons

1995-1996 ===> 150 toms (because production has been increased by 50%)

1996-1997 ===> 600 tons (six times production in 1995)

When we look in to the above calculations, it is very clear that the production of rice has been increased 450 tons in 1996 - 97 from 150 tons in 1996.

Percentage of increase in 1996-1997 = (450/150)X100%

= 3X100%=300%

Hence percentage of rice production increased from 1996 to 1997 is 300%

1995 ===> 100 tons

1995-1996 ===> 150 toms (because production has been increased by 50%)

1996-1997 ===> 600 tons (six times production in 1995)

When we look in to the above calculations, it is very clear that the production of rice has been increased 450 tons in 1996 - 97 from 150 tons in 1996.

Percentage of increase in 1996-1997 = (450/150)X100%

= 3X100%=300%

Hence percentage of rice production increased from 1996 to 1997 is 300%

2. 15% of income of A is equal to 25% of income of B and 10% of income of B is equal to 30% of income of C. If income of C is $ 1600, then total income of A, B and C is :

Let A,B and C be the incomes of A,B and C respectively

From the given information, we have C = $1600

10% of B = 30% of C

(10/100)B = (30/100)X1600

B = $ 4800

15% of A = 25% of B

(15/100)A = (25/100)X4800

A = $8000

A+B+C = 8000+4800+1600 = 14400

Hence, the total income of A,B and C is $14400

From the given information, we have C = $1600

10% of B = 30% of C

(10/100)B = (30/100)X1600

B = $ 4800

15% of A = 25% of B

(15/100)A = (25/100)X4800

A = $8000

A+B+C = 8000+4800+1600 = 14400

Hence, the total income of A,B and C is $14400

3. The length of a rectangle is increased by 50%. By what percent would the width have to be decreased to maintain the same area?

Let the length and width of the rectangle be 100 cm each.

Area of the rectangle = lXW = 100X100 = 10000 cm^{2}

The length of the rectangle is increased by 50%

Let the width of the rectangle be decreased by P% to maintain the same area

After changes, length = 150, width = (100-P)% of 100 = 100-P

Even after the above two changes, area will be same

Therefore 150X(100-P) = 10000

15000 - 150P = 10000 ===> 150P = 5000 ===> P = 33.33%

Hence, the width has to be decreased by 33.33% to maintain the same area

Area of the rectangle = lXW = 100X100 = 10000 cm

The length of the rectangle is increased by 50%

Let the width of the rectangle be decreased by P% to maintain the same area

After changes, length = 150, width = (100-P)% of 100 = 100-P

Even after the above two changes, area will be same

Therefore 150X(100-P) = 10000

15000 - 150P = 10000 ===> 150P = 5000 ===> P = 33.33%

Hence, the width has to be decreased by 33.33% to maintain the same area

4. The production of wheat was increased by 20% from the year 1994 to 1995. It was further increased by 25% from 1995 to 1996. The percentage change in the production of wheat from 1994 to 1996 was

Let 100 tons be the production of wheat in 1994

In 1994 ===> 100 tons

In 1994-1995 ===> 120 tons (20% increment)

In 1995-1996 ===> 150 tons (further 25% increment)

When we look in to the above calculations, it is very clear that the production of wheat has been increased by 50 tons in 1996 from 100 tons in 1994

Percentage change = (50/100)X100 % = 50%

Hence, the percentage change in the production of wheat from 1994 to 1996 was 50%

In 1994 ===> 100 tons

In 1994-1995 ===> 120 tons (20% increment)

In 1995-1996 ===> 150 tons (further 25% increment)

When we look in to the above calculations, it is very clear that the production of wheat has been increased by 50 tons in 1996 from 100 tons in 1994

Percentage change = (50/100)X100 % = 50%

Hence, the percentage change in the production of wheat from 1994 to 1996 was 50%

5. The price of a table is $ 400 more than
that of a chair. If 4 tables and 6 chairs together cost $3600, by
what percentage is the price of the chair less than that of the table ?

Let "x" be the price of a chair. Then the price of a table = x+400

4 tables + 6 chairs = 3600

4(x+400) + 6x = 3600

4x+1600+6x = 3600

10x = 2000 ===>x = 200

So, price of a chair = $400 and price of a table = $800

Price of a chair is $400 less than that of the table

Percentage = (400/800)X100% = 50%

Hence, the price of a chair is 50% less than that of the table.

4 tables + 6 chairs = 3600

4(x+400) + 6x = 3600

4x+1600+6x = 3600

10x = 2000 ===>x = 200

So, price of a chair = $400 and price of a table = $800

Price of a chair is $400 less than that of the table

Percentage = (400/800)X100% = 50%

Hence, the price of a chair is 50% less than that of the table.

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