# APPLICATION PROBLEMS ON PERCENTAGE

What is percentage ?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by whole and multiply by 100.

Hence, the percentage means, a part per hundred. The word per cent means per 100. It represented by the symbol “%”

How to convert the given quantity as percentage ?

To convert the fraction or decimal to percentage, we will multiply it by 100%.

Problem 1 :

Bob has a collection of 450 pens. If he gave 90 pens to his friend Jenny, find the percent of pens left with Bob?

Solution :

Number of pens that Bob has = 450 pens

Number of pens given to his friend = 90

Number of pens left = 450 – 90

= 360 pens

Number of pens left out of the total pen = 360/450

The percent of pens left = (360/450) × 100

= 8% pens

So, the percent of pens is 8% pens is left.

Problem 2 :

How much percentage of a month is a day?

[Take 1 month = 30 days]

Solution :

1 month = 30 days

= 1 day : 30 days

= 1/30

The percentage of a month of a day = (1/30)×100%

= 10/3 %

So, percentage of month is 10/3%.

Problem 3 :

A rectangular tank is filled with kerosene up to 1/3 of its height. Find the percentage of kerosene in the tank.

Solution :

Let h be the height of the tank.

Height reached by kerosene = 1/3 of h

Ratio between the new height to original height.

= 1/3 of h : h

= h/3 : h

= 1/3 : 1

Fractional part kerosene comparing the original = 1/3

The percentage of kerosene in the tank = 1/3 x 100%

= 100/3

= 33.3%

So, the percentage of kerosene in the tank is 33.3 %.

Problem 4 :

In a test, if 30% marks are required to clear the test and Mary has scored 50 marks out of 120, will she clear the test?

Solution :

Required percentage to clear the test = 30%.

Mary has scored = 50 marks out of 120

= 50/120

Converting it as percentage, we get

= (50/120)  x 100%

= 41.66%

So, she can clear the test.

Problem 5 :

Walter has a collection of 56 stamps out of which he gave one-fourth to his friend. Find the percentage of stamps given by Walter to his friend?

Solution :

Number of stamps he has = 56

Number of stamps he is giving to his friend = 1/4 of 56

= 1/4 x 56

= 14

Percentage of stamps given to his friend = (14/56) x 100%

= (1/4) x 100%

= 25%

Problem 6 :

Jack, Ryan and Susan study in three different schools and scored the following marks in math test :

a) Jack – 40/60

b) Ryan – 33/55

c) Susan – 52/65

Can you identify and tell who has performed better?

Solution :

a) Jack's score – 40/60

Converting it as percentage, we get

= (40/60) × 100 %

= (4/6) × 100 %

= 66.67 %

Jack has scored 66.67 % .

b) Ryan's score = 33/55

Converting it as percentage, we get

= (33/55) × 100%

= 60%

Ryan has scored 60% .

c) Susan = 52/65

Converting it as percentage, we get

= (52/65) × 100 %

= 80%

Susan has scored 80% .

So, Susan has performed better in the school.

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