OPERATIONS WITH PERCENTAGE WORD PROBLEMS

Problem 1 :

A house in Kitsilano was sold for 300% of what owners paid. If the owners sold the property for $1.2 million, how much did they originally pay for the house ?

Solution :

Worth of property when owner's sold = 1.2 million

Original price = 300% of 1.2

= (300/100) x 1.2

= 3.6 million

Problem 2 :

Alice Wong contributed $36 towards a birthday present that cost a total of $80. What percent of the total did she contribute?

Solution :

Alice wong's contribution = $36

Worth of birthday present = $80

36 is what percentage of 80,

Let x be the required percentage.

x% of 80 = 36

(x/100) ⋅ 80 = 36

8x/10 = 36

x = (36 ⋅ 10)/8

x = 45%

So, he contributed 45% of total.

Problem 3 :

$475 is what percent more than $125?

Solution :

Let x be the required percentage.

x% of 125 = 475

(x/100) ⋅ 125 = 475

x = (475 ⋅ 100)/125

x = 380

100 + 280 = 380

So, 280% more of 125.

Problem 4 :

$530 is what percent less than $643.95?

Solution :

Let x be the required percentage.

x% of 643.95 = 530

(x/100) ⋅ 643.95 = 530

643.95x/100 = 530

x = 530 (100) / 643.95

x = 82.30

100 - 82.30 ==> 17.69

Approximately 17.7% less than 643.95

Problem 5 :

In Quebec, a motorcycle sold for $28,461.38 including 5% GST and 7.5% PST. How much did the motorcycle cost before tax?

Solution :

GST = 5% 

PST = 7.5%

Total = 12.5%

Amount of be paid = 12% less than the original

Let x be the amount before tax.

(100 + 12.5)% of x = 28,461.38

112.5% of x = 28,461.38

x = 28461.38/1.125

x = 25299

So, the original amount before tax is 25299.

Problem 6 :

A bartender whose salary was $320 per week was given a raise of $40 per week. What percent increase did the bartender receive?

Solution :

Salary = 320

The amount he is wishing to raise = 40

Let x be the required unknown percentage.

x% of 320 = 40

320x/100 = 40

32x/10 = 40

32x = 400

x = 400/32

x = 12.5

So, the raise is 12.5% of salary.

Problem 7 :

A credit card carries a 15.2% interest rate. If the amount of interest accrued for last month was $360, what is the balance on the card?

Solution :

Let x be the balance.

Interest = 15.2%

Interest accrued = 360

15.2% of x = 360

0.152x = 360

x = 360/0.152

x = 2368.42

Problem 8 :

Revenue increased from $1,062 last year to $1,947 this year. What was the percent increase in profit?

Solution :

Percentage increase or decrease

= |old value - new value| / old value x 100%

Old value = 1062, new value = 1947

= {|1947 - 1062| / 1062} x 100%

= (885/1062) x 100%

= 0.833 x 100%

= 83.3%

Problem 9 :

Net income in November increased 18 ½% over October’s net income. If net income for October was $25680, what was net income for November?

Solution :

Net income = 25680

Increases by 18 1/2%

Income after November = (100 + 18.5)% of 25680

= 18.5% of 25680

= 1.185 x 25680

= 30430.8

So, the income after November is 30430.8

Problem 10 :

The CPI at the end of 2010 was 15% lower than at the end 2000. What was the CPI at the end of 2010, if the CPI at the end of 2000 was 120?

Solution :

CPI amount at the end of 2000 = 120

85% of 120 = CPI amount at the end of 2010.

= (85/100) x 120

= 0.85 x 120

= 102

Problem 11 :

The earnings per share (EPS) of a company last year was $1.12. This year the earnings per share is $1.40. What is the percent change in EPS? What is the new EPS as a percent of the old EPS?

Solution :

Earning last year = 1.12 (old value)

Earning this year = 1.40 (new value)

Percentage change = { (1.40 - 1.12)/1.12 } x 100%

= (0.28 / 1.12) x 100%

= 0.25 x 100%

= 25%

So, the percentage change is 25%.