# CLASS-8PROFIT & LOSS - PROBLEM & SOLUTION

Example.1) A man buys some fruit for \$ 150 and sells it for \$ 225, find the profit and percentage of profits.

Ans.) As per the given condition, the man purchase some fruit for \$ 150 and sells it for \$ 225

So, the person makes profit = 225 – 150 = \$ 75

( SP - CP ) / Profit

Percentage of profit = ----------------------- X  100

Purchase Price / CP

\$ 75

=  ------------  X 100                                                                                                                                                  \$ 150

\$ 75

=  -----------  X 100  =  50 %

\$ 150

So, the person makes a profit of around \$ 75 by 50% profits  (Ans.)

Example.2) A shopkeeper bought chocolate at the rate of 6 for \$ 5 and sold them at the rate of 5 for \$ 6.

a) What kind of percentage of profit he has done?

b) How many chocolate would he have to sell to earn a profit of \$ 55?

Ans.)  Cost Price (CP) of 6 chocolates = \$ 5,

5

So, CP of 1 chocolate = ---------- \$

6

Sell Price (SP) of chocolate is at the rate of 5 chocolate = \$ 6

6

So, CP of 1 chocolate = ---------- \$

5

So the profit per chocolate

6              5

=  --------- - ---------

5              6

36 – 25             \$ 11

=  ------------  =  ----------

30                 30

Profit

Now, profit percentage = -------------- X 100

CP

11 / 30

= --------------  X 100

5 / 6

11            6

= -------- X -------- X 100 = 44 % …………………(1)  (Ans.)

30            5

Now as per the condition,  we have to quantify the number of chocolate to get the profitability of about \$ 55.

11

He can earn profit of \$ --------- to sell 1 chocolate

30

1              30

To earn \$ 1 by selling = ---------- = ---------

11 / 30          11

30

To earn \$ 55 profit hr has to sell = --------- X  55                                                                                                                                                       11

= 150 chocolates

So, if he would like to earn a profit of \$ 55 then he has to sell 150 chocolate.            (Ans.)

Example.3) A man sold his computer for \$ 330 at the profit of 10%, then find out what did the computer cost him?

Ans.) As per the given condition, the person has sold the computer by \$ 330 at a profit rate of 10%

Suppose the cost price of the computer is Z

10

He has done the profit 10% =  Z X ---------

100

Z

= ----------                                                                                                                                                             10

Z

So, now as per the condition ,    Z + --------- = 330

10

11 Z

Or, ---------- = 330

10

330 X 10

Or,  Z =  -------------- =  \$ 300                                                                                                                                                11

So, the cost of the computer is  \$ 300.     (Ans.)

Example.4) A typewriter was bought for \$ 250, find its selling price if it is sold at a) Profit of 15 % and loss of b) 12 %

Ans.) As per the given condition, the value of a typewriter is \$ 250.

If he sold the typewriter of 15% profit then the value would be

15

= \$ ( 250 + 250 X --------- )                                                                                                                                                           100

=  \$ ( 250 + 37.5 ) =  \$ 287.5……………………..(a)      (Ans.)

If he sold the typewriter by 15% profit then the value would be

12

=  \$ ( 250 - 250 X --------- )                                                                                                                                                           100

=  \$ ( 250 - 30 ) =  \$ 220 …………………….…(b)  (Ans.)

Example.5) By selling a calculator for \$ 320, a shopkeeper incurred a loss of 20%, what was the cost price of the calculator for him?

Ans.)  As per the given condition, shopkeepers have made a loss of 20% to sell the calculator by \$ 320

Suppose the cost price of the calculator is A

If he get loss by 20%, then

The actual cost price of the calculator is =>

20

A – ( A X ---------- ) = 320                                                                                                                                                  100

A

Or, A – --------- =  320

5

4A

Or,  ---------- = 320

5

320 X 5

Or,   A = --------------  =   80 X 5 =  400                                                                                                                                   4

So, the actual value or cost price of the calculator is \$ 400.    (Ans.)

Example.6) Mr. Richard sold two printers for \$ 200 each, on one of the printers he made a profit of 20%, and on the others he incurred a loss of 20%, find the total loss or gain and also the net loss or gain percent.

Ans.) As per the given condition, for the 1st printer -

Let, the price (CP) of the printer is A

He has sold the printer at \$ 200 and made a profit of 20%.

20

So, as per the given condition A + A X --------- = \$ 200

100

A

Or,    A + ---------- =  200

5

6A

Or,  ---------- = \$ 200

5

5

Or, A =  \$ 200 X -------- =  \$ 166.66 = \$ 167   (CP)                                                                                                                              6

As per the given condition, for the 2nd printer -

Let, the price (CP) of the printer is A

He has sold the printer at \$ 200 and made a loss of 20%.

20

So, as per the given condition  A – A X ---------- =  \$ 200                                                                                                                                                100

A

Or,    A – -------- =  200

5

4A

Or,  ----------  =  \$ 200

5

5

Or, A =  \$ 200 X --------- =  \$ 250     (CP)                                                                                                                                         4

So, as per the requirement –

Total Cost price (CP) of two printers is = \$ 167 + \$ 250

= \$ 417

Total Sell price (SP) of two printers is = \$ 200 + \$ 200

= \$ 400

Here we can observe that, total sell price which is \$ 400 is less than the total cost price which is \$ 417.

So, we can conclude here he has lost by = \$ 417 - \$ 400

=  \$ 17

\$ 17

So, as per the percentage he has loss by = ---------- X 100                                                                                                                                                   \$ 417

=  4.07%  =  4 %

So, Mr. Richard has made the loss by \$ 17 as the percentage of 4%. (Ans.)

Example.7) If a man incurs a loss of 20% by selling an article for \$ 800, at what price should he sell it to make a profit of 15%

Ans.) as per the given condition, the man has sold out the product by \$ 800 with a loss of 20%

If, we consider the price of the product is Z and he has made a loss of 20%

So, as per the given condition –

20

Z – Z  X --------- = \$ 800

100

Z

Or,       Z – -------- =  \$ 800

5

4 Z

Or,      ----------  =  \$ 800

5

\$ 800 X 5

Or,    Z  =  --------------  =  \$ 1000

4

So, the cost price (CP) of the product is \$ 1000.

Now, if he wish to profit at the percentage of 15%, then the Sell Price (SP) would be as follows –

15

\$ 1000 + \$ 1000 X -------- =  \$ 1000 + \$ 150 = \$ 1150

100

So, the person should sell the product for \$ 1150 to get a profit of 15%.  (Ans.)