APPLICATION PROBLEMS ON PERCENTAGE

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.

Problem 7 :

Last week, you finished Level 2 of a video game in 32 minutes. Today, you finish Level 2 in 28 minutes. What is your percent of change?

Solution :

Percentage change = (New value - Old value)/Old value x 100%

Time taken last week = 32 minutes

Time taken today = 28 minutes

= (32 - 28) / 28 x 100%

= (4/28) x 100%

= 14.2 %

Problem 8 :

Explain why a change from 20 to 40 is a 100% increase, but a change from 40 to 20 is a 50% decrease

Solution :

Percentage change = (New value - Old value)/Old value x 100%

Old value = 20, new value = 40

Percentage change = (40 - 20) / 20 x 100%

= (20/20) x 100%

= 100% 

Old value = 40, new value = 20

Percentage change = (20 - 40) / 40 x 100%

= (-20/40) x 100%

= -50% 

50% decrease.

Problem 9 :

Donations to an annual fundraiser are 15% greater this year than last year. Last year, donations were 10% greater than the year before. The amount raised this year is $10,120. How much was raised 2 years ago?

Solution :

Let x be the fund a year before. It shoud be 100%.

Last year denomination = 110% of x

This year denomination = 115% of 110% of x

This year denomination = 10120

10120 = 115% of 110% of x

10120 = 1.15(1.10x)

x = 10120 / 1.15(1.10)

x = 8000

So, 2 years ago the fund is $8000.

Problem 10 :

Forty students are in the science club. Of those, 45% are girls. This percent increases to 56% after new girls join the club. How many new girls join?

Solution :

Number of students in the science club = 40

Number of girls = 45% of 40

= 0.45(40)

= 18 girls were there in 40 students.

Let x be the number of new gilrs joining in the club.

18 + x = 56% of (40 + x)

18 + x = 0.56(40 + x)

18 + x = 22.4 + 0.56x

x - 0.56x = 22.4 - 18

0.44x = 4.4

x = 4.4/0.44

x = 10

So, number of new girls joining is 10.