Profit and Loss, Simple Interest //Percentage / Math / Solution

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 

                     = 3000

Decrease 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

                                                           = 611

Notice 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 ) = 115

His 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