**Definition of cost price and selling price**: The purchasing price of anything is called cost price and the selling price of that thing is called selling price.

Or, The expenditure which is done for buying or manufacturing commodities is the cost price and the price that is obtained by selling commodities is the selling price.

**Definition of profit**: If the selling price is more than the cost price then it’s called profit. The amount by which the S.P is greater than the C.P is the amount of profit.

∴profit= Selling price (S.P)– Cost price(C.P)

**Definition of loss**: If the selling price is less than the cost price then it’s called loss. The amount by which the C.P is greater than the S.P is the amount of loss.

∴Loss=Cost price- Selling price

Some formula for profit and loss:

- profit= Selling price (S.P)– Cost price(C.P)
- Selling price (S.P)= Cost price(C.P)+ profit
- Cost price(C.P)= Selling price (S.P)– profit
- Loss=Cost price- Selling price
- Cost price = Selling price + Loss
- Selling price = Cost price –Loss

*** For comparison, profit or loss is expressed as percentage. Profit or loss is always calculated in terms of cost price.

Ex: **On selling a commodity, profit of a wholesale seller is 20% and profit of retail seller is 20%. If the retail selling price of the commodity is tk. 576, what is the cost price of the wholesale seller?**

Solution: given,

The selling price of commodity is 576 taka

Profit of a retail seller is 20%

We need to find cost of wholesale seller=?

In 20% profit selling price of retail seller = (100+20) taka

=120 taka

If selling price 120 taka cost price is 100 taka

∴If selling price 1 taka then cost price is 100/120 taka

∴ if selling price 576 taka then cost price is (1oo×576)/120=480 taka

Selling price of wholesale seller 480 taka

In 20% profit selling price of wholesale seller = (100+20)= 120 taka

If selling price 120 taka then cost price is 100 taka

∴ If selling price 1 taka then cost price is 100/120 taka

∴ If selling price 480 taka then cost price is (100×480)/120=400 taka

∴cost price of wholesale seller 400 taka

Answer: 400 taka.

**Ex: A shopkeeper sold some amount of pulses for Tk. 2375 at the loss of 5%. What would be the selling price of pulses to make a profit of 6%?**

Solution:

In 5% loss selling price = (100-5) taka

=95 taka

In 6% profit selling price = (100+6) taka

=106 taka

If 95 taka is selling price then cost price is 100 taka

∴ If 1 taka is selling price then cost price is 100/95 taka

If 2375 taka is selling price then cost price is (100×2375)/95 = 2500 taka

When 100 taka is cost price then selling price is 106 taka

∴ When 1 taka cost price then selling price is 106/100 taka

∴ When 2500taka is cost price then selling price is (106×2500)/100 taka

= 2650 taka

∴ The selling price would be 2650 taka

Answer: 2650 taka

**Ex: Equal number of bananas is bought at 10 and 15 pieces per Tk. 30 and all the bananas are sold at 12 pieces per Tk. 30. What will be the percentage of profit or loss?**

Solution:

The cost of 10 bananas is 30 taka

∴ The cost of 1 banana is 30/10 taka

∴ the cost of 60 bananas is (30×60)/10 taka

=180 taka

Again,

The cost of 15 bananas is 30 taka

∴The cost of 1 banana is 30/15 taka

∴ The cost of 60 bananas is (30×60)/15 taka

=120 taka

∴the cost of (60+60) or, 120 bananas

=180+120)=300 taka

But,

The selling price of 12 bananas is 30 taka

∴The selling price of 1 banana is 30/12 taka

∴ The selling price of 120 bananas is (30×120)/12 taka

=300 taka

∴so the cost price and selling price of 120 bananas 300 taka

Ans: There is no profit or loss.

**Ex: If the percentage of profit is Tk.10.50 per annum, what will be the profit for Tk. 2000 in 5 years?**

**In 100 taka 1 year profit is 10.50 taka**

∴ In 1 taka 1 year profit is 10.50/100 taka

∴ In 2000 taka 5 years profit is (10.50×2000×5)/(100×100) taka

= (1050×2000×5)/(100×100) taka

=1050 taka

∴ Profit is 1050 taka

Ans:1050 taka

**Ex: If the percentage of profit per annum is decreased from Tk.10 to Tk 8, how much less will be the profit of Tj. 3000 in 3 years?**

Solution:

For 100 Taka in 1 ywar profit decreased by (10-8) taka

=2 tka

∴For 1 taka in 1 year profit decreased by 2/100 taka

∴For 3000 taka in 3 years profit decreased by (2×3000×3)/100 taka

=180 taka

∴Profit decreased 180 taka

Ans: 180 taka