Discount:

Percentage:

Simple Interest

Q.1. a scarf priced at $100 is sold for $88. Find the percentage discount.

Solution:

                    Discount    =  Marked Price - Sale Price
                                        =  $100 - $88
                                         = $12


                       Percentage discount = 12/100  x 100%
                                                            = 12% Ans.

 



Q.2. A laptop is sold for $1274 after a discount of 9%.
i) Find the marked price of the laptop.

ii) If a 5% discount is given on the marked price of the laptop before it is sold at a further discount of 4%, would the sale price still be $1274? Show your working clearly.

Solution:

                     92 % of the marked price = $1274

                      1% of the marked price = $1274/92

                 100% of the marked price    = $1274 /92   x 100

                                                                 = $1384.78

                   The marked price of the laptop is  $1384.78.


       ii)     Sale price of laptop after a 5% discount = 95/100 X  $1384.78

                                                                                    = $1325

        Sale price of laptop after a further discount of 4%  = 96/100 x $1325

                                                                                               = $1262.4                                                                 

                    No, the sale price would not be $1262.4


Q.3. A sculpture is sold for $533 after a discount of 18%.
i) Calculate the marked price of the sculpture.
ii) If a 10% discount is given on the marked price of the sculpture before it is sold at a further discount of 8%, would the sale price still be $ 533? Show your working clearly.

Solution:

I) 82% of the marked price = $533

  1% of the marked price     =  $533/82

  100% of the marked price  = $533/82   X  100

                                                = $650

The marked price of the sculpture is $650.

ii)     Sale price of sculpture after a 10% discount = 90/100 X  $650

                                                                                    = $585

Sale price of sculpture after a further discount of 8% = 92/100 x $585

                                                                                           = $538.20

                                                                                          

                    No, the sale price would not be $533.


Q.4. The marked price of a washing machine is $600. A discount of 6% is given during a sale. Find the sale price of the washing machine.

Solution:

           Discount  = Marked Price - rate of Discount
                           = $600 - $.06
                           = $36

               Sale price     =  Marked price - Discount

                                      = 600  - 36
                                      = 564   Ans.














Simple Interest

Interest: 

The amount collected or paid for the use of money
To calculate simple interest, you use the formula:

                        I = p.r.t


Principal:

the amount of money borrowed or deposited

Rate:

the interest percent per year as a decimal

Time:

time in years that the money earns interest





Q.1. Jose deposits $1500 of his tax refund into an account that earns simple annual interest. How much interest will his account earn after 6 years at an annual interest rate of 4%?

             = $1500  × 6 × 0.04

            = $360


The following clients have opened savings accounts with the State Employees Credit Union. 
Use the simple interest formula I = p.r.t to calculate the principal, rate, time, or interest earned by each client. 

Calculate the interest to the nearest cent, and write your answers in the chart below.




Q.2. If Sheila got a 5-year $5,800 loan at an interest rate of 10% 
         for her first car, how much interest did she pay?

  I = p.r.t
   = $5,800 X o.1 X 5
   = $2,900


Q.3. Lisa borrows $2850 at 4.3% simple interest per year. 
When Lisa pays the loan back 9 years later. 
What is the total amount that Lisa ends up repaying?


I = p.r.t

  = $2850 X 0.043 X 9

  = $1102.95


Use the simple interest formula to solve each problem. Show your work!

Q.1. Lorel deposits $7,500 into the bank. She does not withdraw or deposit money for 6              years. 
     She earns 6% interest during that time.

a. How much interest will she have earned at the end of 6 years?

     interest = $7,500 X 6 X .006

               = $270


b. What will the balance be when she is finally able to withdraw her money?

_______


Q.2. Cara just purchased a new car. He financed $45000 and must pay it back over 5              years with 11% interest.

       a. How much will Cara have paid in interest by the time his car is paid off?
        b. How much will he have paid for his car. Including interest, after 5 years?



3. Dina has a balance of $10,200 on his credit card. 

     He threw the card away so he can never use it again. 

     He has 3.5 years to pay off the balance. The interest rate on his card is 21%.

a. At the end of the 3.5 years. how much interest has he paid?


b. When Dina pays off his credit card, how much will he have paid in all?

                                                              🏆⚽

Q.4. Travel to Qatar for the FIFA 2022 finals
The bank agrees to give you a loan of $4,000 with 1% simple interest over 2 years. How much will your monthly payments be?

                                                                🏈🏆


Q.5. Travel to Phoenix for the 2023 Super Bowl
The bank agrees to give you a loan of $3,000 with 2% simple interest over 1 year. How much will your monthly payments be?




Q.6. The bank agrees to give you a loan of $2455,000 with 2% simple interest over 12 years. How much will your monthly payments be?

                                        🚗 🚙

Q.7. The bank agrees to give you a loan of $45,000 with 2% simple interest over 5 years. How much will your monthly payments be?





Percentage Word Problem 

(Discount)

Very often, retailers are not able to sell defective merchandise, overstocked items, or discontinued models at retail selling prices. To clear the merchandise in stock, the items are usually sold at a lower price, called the sale price. The difference between the original selling price, also known as the marked price, and the sale price is called the discount:

            Discount = marked price - sale price

The discount is often given as a percentage of the marked price:

               Discount / Marked price  x 100%

Q.1. A watch priced at $160 is sold for $100. Find the percentage discount.

Solution:

Discount = marked price - sale price
              = $160 - $100
              = $60
Percentage discount  = $60/$160  x 100%
                                      =   37.5%

Q.2. The marked price of a washing machine is $600. A discount of 6% is given during a sale. Find the sale price of the washing machine.

Solution:

Discount  = marked Price  X  Rate of Discount
                = $600  X  .06
                = $36

Sale Price   =  Marked Price -  Discount
                    =  $600  - $36
                      = $564 Ans.



 


Q.1. A laptop priced at $150 is sold for $100. Find the percentage discount.

Solution:

Discount = marked price - sale price
                = $150 - $100
                = $50

Percentage discount  = $50/$150  x 100%
                                     =   33.3% 

Q.2. A sculpture is sold for $533 after a discount of 18%. 
i) Calculate the marked price of the sculpture.
ii)  If a 10% discount is given on the marked price of the sculpture before it is sold at a further discount of 8%, would the sale price still be $533? Show your work clearly.

Solution:
i) 82% of the marked price = $533

1 % of the marked price =  $533/82

100% of the marked price = $533/82 x 100
                                            = $650

The marked price of the sculpture is $650.

ii) Sale price of sculpture after a 10% discount = 90/100 x $650 
                                                                                = $585

The sale price of the sculpture after a further discount of 8% = 92/100 x $585 
                                                                                           = $538.20

N0, the sale price would not be  $533.

Percentage Word Problem

Percentages are useful in conveying information in everyday life. The symbol, % is used to represent 'percent'.

Thus 50 %  is read as '50 percent.






Suppose the sales of a company last year were $ 100 million and the sales of the company this year are $200 million. The sales of the company this year are 200/100  =  200% of its sales last year.

Expressing a Percentage as a Fraction:


a) Express each of the following percentages as a fraction.
i) 88%
= 88/100
= 22/25

ii) 128 %
= 128 /100
=  32/25

iii) 0.5%
= 0.5/100
= 1/200

b) Express each of the following fractions as a percentage.
i)  1/2
=  1/2   X    100%
=   50%

ii)  9/8
=   9/8   X  100%
=  900/8 %
=  112.5 %

a) Express each of the following percentages as a fraction.
i)  45 %
=  45/100
= 9/20

b) Express each of the following fractions as a percentage.
i) 17/20
=  17 / 20  X100
= 85 %

Q.2. Express each of the following percentages as a decimal.
i) 85%
= 85 / 100
= 0.85

Express each of the following decimals as a percentage.
i) 0.16
= 0.16 X 100%
= 16%

Q.1. A class has 40 students. Given that 75% of them passed a Mathematics​ test. Calculate the number of students who failed the test. 

Solution: 

Percentage​ of students who failed the test = 100% - 75 %
                                                                  = 25%
 Number of students who failed the test = 25% x 40 
                                                                 = 0.25 x 40
                                                               = 10 Ans.


2. A school has 1500 students. Given that 3% of them were late for school on a particular day, find the number of students who were punctual for school. 

Solution:

Number of students who are late for school = 3% of 1500 
                                                               = 3/100 x 1500 
                                                               =
 Number of students who are punctual for school = 1500 – 45 
                                                                        = 

 Q.3. 1800 people attended the National Day dinner in a certain constituency. Given that 35.5% of them were men, 40% of them were women and the rest were children, find the number of children who attended the dinner.

Solution:

Number of men = 35.5/100 x 1800 
                            = 639 
Number of women = 40/100 x 1800 
                               = 720 
Total number of men and women = (639 + 720) 
                                                       = 1359 
                 Number of children    = 1800 – 1359 

Q.4. In 2011, 600 out of 1600 people passed the entrance test of a school. 400 out of 1000 people passed the entrance test of the same school in 2012. In which year did a higher percentage​ of people pass the entrance test of the school?


 Percentage​ of people who passed the entrance​ test​ in 2011 = 600/1600 x 100% 

Percentage of people who passed the entrance test in 2012 = 400/1000 x 100% 

A higher percentage of people passed the entrance test of the school in 2012

Q.5. There were 30,000 people in city A and 4000 people attended its New year party. There were 25,000 people in city B and 2800 people attended its New Year party. Which city had a higher percentage of people attending its party?


 Percentage of people who attended party in city A = 4,000/30,000 x 100 

Percentage of people who attended party in city B = 2800/25,000 x 100 

 A higher percentage of people attended its party in city A

 

 

Conversions Involving Percentages:

iv) Converting Percentage to Decimal numbers: 

Represent 60% as a decimal number 60 %     = 60 out of 100 
                                                                         = 60/100
                                                                         = 6/10
                                                                       = 0.6 

iii) Converting Percentage to Fractions: 

Represent 38% as a fraction. 38 %      = 38 out of 100
                                                             = 38/100 
                                                            = 19/50 


ii) Converting Decimal Numbers to Percentages: 

a) Represent 0.63 as a percentage. 

Conversions Involving Percentages: Fractions to Percentages
Represent ¾ as a percentage.

Percentage Word Problem: 

Q1. Rama bought a pen for $5. If she had $20 in her pocket, what percentage of the money did she spend on the pen? 

Solution:

Money spent by Rama = $5 out of $20 = 5/20 x 100 
                                     = 25 % 

Ans: 25%

Q2. 40% of 1 kg is how many grams?

Solution: 

1 kg = 1000 g 

40% of 1000 g = 40/100 x 1000 = 400 gm

Ans: 400gm

Q3. A tank had 80 L of water. 20% of the water was drained out. How many litres of water remained in the tank?

Solution: 

Water drained out = 20% of 80 L = 20/100 x 80 = 16 L 

Water left in the tank = 80L - 16 L = 64 L

Ans: 64L

Q4. Monica runs 100 m in 12 seconds. Kanika takes 5% more time to run 100m. 
How much time does Kanika take?

 Solution: 

5% of 12 seconds = 5/100 x 12 = 0.6 Seconds

Time taken by Kanika = 12 + 0.6 = 12.6 seconds

Ans: 12.6seconds.

Percentage 

The price at which an item is bought is known as its Cost Price.
The price at which an item is sold is known as its  Selling Price.

Profit and Loss: 

When the Selling Price is more than the Cost price, there is a profit.

Profit = Selling Price – Cost Price 

The price at which an item is bought is known as its Cost Price

 The price at which an item is sold is known as its Selling Price.

Profit = Selling Price - Cost Price

Profit = S.P.  - C.P.

Loss = Cost Price - Selling Price






 
                

                
                                   


            Ex. 1. Find the profit or loss in each case.

                       a) CP  = $420
                           SP  = $615

               Solution:
                  As selling price is more than cost price.

                                  Profit = SP  - CP
                                          = $615 - $420
                                          = $195


           b) CP = $6348  and SP = $6000

            Solution:

            As cost price is more than the selling price.

                         Loss  = CP - SP

                                 = $6348 - $6000
                                 = $ 348

Increase percent:

Suppose there are 100 pupils in a school and the number increases by 10%. This means an increase of 10 in the number of pupils and a new total of 110 pupils. Whatever the number of pupils in the school, the ratio of the new total to the old total will always be the same for an increase of 10%.

The new total: the old total  = 110: 100.
      the new total = 110/100  X the old total
       the old total  = 100/110 X the new total.
Also, the ratio of the increase to the new total is   10: 110.
   the increase = 10/110  X  the new total

Q. A man's salary is $ 700. If it increases by 8%, find his new salary.

New salary : old salary  = 108 : 100     new salary  = 108/100  X old salary                        = 108/100  X $700                           = $ 756

Q.2. During 1960, the population of a village increased by 12%. If the population at the end of the year is 3360, find the population at the beginning of the year.

Solution:
New population : old population  = 112 : 100
old population = 100/112  X new population                     = 100/112  X 3360                       = 100 X 30                      = 3000Decrease percent:Now suppose that a fruit grower's crop of apples decreases by 10%. Where he grew 100 kg of apples, he now grows 90 kg. 
             new crop : old crop  = 90  : 100
    Q.1. During q year, the number of pupils in a school decreases by 6%. The number at the beginning of the year was 650. Find the number at the end of the year.

The number at the beginning: number at end  = 100: 94
The number at the end of the year = 94/100  X 650                                                          = 47 X 13                                                           = 611Notice that this problem can be solved by finding the decrease and subtracting.

Ex- 39A


Q.1. The number of books in a library is 12,500. If the number is increased by 8%, how many books will there be in the library?

Solution: With 8% increment, 100 books increased to (100 + 8) or 108.
    With 8% increment, the number of books are                  = 108/100  X 12500
                 = 13,500  Ans.
2. a worker earns $15 in a week, but increases this by 15% by overtime. Find his earnings during a week when he worked overtime.

Solution:

By overtime, his earnings with 15% increment become =                               (100 + 15 ) = 115His earning during overtime              = 115/100 X $15              = $69/4              = $17.25 Ans.
8. A certain number decreased by 22% equals 390. Find the number.
Solution:With 22% decrease, the number decreases from 100 to                  (100 - 22)                   = 78
But the number decreases to 390
 The number is = 100/78 X 390                          = 500 Ans.
9. Tom earns 10% more than Harry. If the difference between their wages is $1.50 per week, find how much Tom earns in a week.

Solution:Tom earns 10% more than Harry
Toms earning = 100/10  X 1.50                    = 15

10. A number when decreased by 42 is decreased by 12%. Find the number.

Solution:
With 12% decrease, the number decreased by 42.The number is = 100/12  X 42                      = 350 Ans.

Ex- 40A


3. A shopkeeper lost 30% by selling an article for $2.80. What did he lose?

Solution:
The Shopkeeper's loss  = 30/100  X 2.80
                                       = 8.40/10
                                       = 0.84

5. A dealer gains $8 when he sells an article to gain 16%. Find the selling price.


Ans: At a 16% gain, the dealer gain 8

His selling price  = 100/16  X 8
                                   = 50 Ans.

 1. Prakash bought a used watch for $100 and spent $50 on its repair. After repairing, it was sold to Kanika for $200. Find the profit or loss suffered by Prakash. 

                 Solution:

                            Cost Price = $100 
                                      Total Cost Price 
                                        = C.P. + overhead expenses 
                                      = $100 + $50 
                                      = $ 150 
                    As S.P. is more than the C.P. Profit 
                                     = $ 200 – $ 150 

                                     = $ 50 

Q.2. A grocer buys a sack of rice for $ 840 and was able to sell it for $820. Find the grocer’s gain or loss. 
             Solution: 

               Selling Price = $ 820 Cost Price 
                                   = $840 
                  As C.P. is more than S.P. Loss 
                                  = $840 - $820 
                                 = $20 Ans 

Q.3. Mina sells a cupboard for $110 and makes a profit of $15. What was the cost price of the cupboard?

Solution:

             S. P. = $110 Profit 
                      = $ 15 C.P. 
                      = S.P. - Profit 
                     = $ 110 - $15 
                     = $ 95 Ans.


Interest: The amount collected or paid for the use of money

To calculate simple interest, you use the formula:

                             I = p.r.t

Principal: the amount of money borrowed or deposited

Rate: the interest percent per year as a decimal

Time: time in years that the money earns interest

Q.1. Jose deposits $1500 of his tax refund into an account that earns simple  annual interest. How much interest will his account earn after 6 years at an annual interest rate of 4%?

                                            I = p.r.t

                                                    = $1500 . 4/100  . 6

                                              =  $360

Q.2. If Sheila got a 5-year $5,800 loan at an interest rate of 10% for her first car, how much interest did she pay?

                          I = p.r.t

                 = $5,800 X o.1 X 5

                        = $2,900

Q.3. Lisa borrows $2850 at 4.3% simple interest per year. When Lisa pays the loan back 9 years later. What is the total amount that Lisa ends up repaying?

                       I = P.R.T

                  = $2850 X 0.043 X 9

                 = $1102.95

THE TOTAL AMOUNT THAT LISA ENDS UP REPAYING  = ($2850 + $1102.95)

= $3952.95


 






 

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