PROBLEMS ON SELLING PRICE AND COST PRICE

Example 1 :

Complete the following table :

Solution :

(a)  Cost price  =  $60

Profit  =  $25

Since profit happens,

Selling price > Cost price

Selling price  =  Cost price + profit

Selling price  =  60 + 25  ==>  $85

So, the required selling price is $85.

(b)  Selling price  =  $195

Loss  =  $35

Since loss happens, 

Cost price > Selling price

Cost price  =  Selling price + Loss

Cost price  =  195+35  ==>  230

So, the required cost price is $230.

(c)  Cost price  =  $275

loss  =  $95

Since loss happens,

Cost price > Selling price

Selling price  =  Cost price - loss

Selling price  =  275 - 95  ==>  $180

So, the required selling price is $180.

(d)  Selling price  =  $297

Profit   =  $135

Since profit happens, 

Selling price > Cost price

Cost price  =  Selling price - profit

Cost price  =  297-135  ==>  162

So, the required cost price is $162.

Example 2 :

Find the selling price for goods bought for :

a)  $500 and sold for a 20% profit

b)  $350 and sold at a 25% loss

c)  $4500 and sold for a profit of 8%

d)  $8000 and sold at a loss of 35%

Solution :

(a)  Cost price  =  $500

Profit  =  20%

Selling price  =  120% of 500

=  1.20(500)

=  600

So, selling price of the goods is $600.

(b)  Cost price  =  $350

Loss  =  25%

Selling price  =  75% of 350

=  0.75(350)

=  $262.5

So, the selling price is  $262.5

(c)  Cost price  =  $4500

Profit  =  8%

Selling price  =  108% of 4500

=  1.08(4500)

=  $4860

So, the selling price is $4860.

(d)  Cost price  =  $8000

Loss  =  35%

Selling price  =  65% of 8000

=  0.65(8000)

=  $5200

So, the selling price is $5200.

Example 3 :

Jacki bought a sewing machine for $560 and sold it for a profit of 18%. At what price did she sell the sewing machine?

Solution :

Cost price of sewing machine  =  $560

Profit made  =  18%

Selling price  =  118% of 560

=  1.18(560)

=  $660.8

Example 4 :

A microscope was purchased for $600 and sold two months later for $450 : Find the loss as a percentage of the cost price

Solution :

Price of microscope when it is purchased = $600

Selling price = $450

Cost price > Selling price

Loss = cost price - selling price

= 600 - 450

= 150

Loss% = (loss amount / cost price) x 100%

= (150/600) x 100%

= (1/4) x 100%

= 25%

So, the loss percentage is 25%.

Example 5 :

I bought a bicycle for $640 and sold it for a profit of 20%. Find the selling price of the bicycle.

Solution :

Cost price of the bicycle = $640

Profit = 20%

Let cost price be 100%. Since the profit is 20%, then 120% of the cost price will be the selling price.

Selling price = 120% of 640

= 1.20(640)

= $768

Example 6 :

A green grocer bought 200 kg of oranges for $180 and sold them for $1:14 per kilogram.

Find:

a) his profit

b) his percentage profit on the cost price.

Solution :

Quantity of oranges = 200 kg

Price = $180

Selling price per kg of orange = $1.14

a)  Selling price of 200 kg = 1.14(200)

= 228

Selling price > cost price

Profit = Selling price - cost price

= 228 - 200

= 28

b) Profit percentage = (Profit / Cost price) x 100%

= (28/200) x 100%

= 14%

Example 7 :

A house was bought for $385 000 and sold for a profit of 10%. For how much was it sold?

Solution :

Price of house = $385 000

Profit = 10%

Original price be 100%, after 10% profit the new price will be 110% of original price.

= 110% of 385000

= 1.10(385000)

= $423500

Example 8 :

Find the percentage profit when a car bought for $7000 is sold for $8470.

Solution :

Cost price of car = $7000

Selling price = $8470

Percentage profit = (Profit / Cost price) x 100%

Profit = Selling price - Cost price

= 8470 - 7000

= 1470

Percentage profit = (1470/7000) x 100%

= 21%

Example 9 :

If 45% of a person’s mass is 36 kg, what is the person’s total mass?

Solution :

45% of total mass = 36 kg

Let x be the total mass.

45% of x = 36

0.45(x) = 36

x = 36/0.45

x = 80 kg

Example 10 :

A dress was bought for $160 and sold for $136. Find the percentage loss on the cost price.

Solution :

Cost price of dress = $160

Selling price = $136

Selling price < cost price

Loss = Cost price - selling price

= 160 - 136

= 24

Loss percentage = (loss/cost price) x 100%

= (24/160) x 100%

= 15%

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