Profit and Loss - Imporant Maths Formulaes

Important Formulas Profit and Loss

1. Cost price and selling price

Cost price (CP) is the price at which an article is purchased.

Selling price (SP) is the price at which an article is sold.

2. Profit and loss

If selling price is more than cost price, profit(gain) occurs.

If selling price is less than cost price, loss occurs.

In case of profit,

profit = selling price – cost price

selling price = cost price + profit

cost price = selling price - profit

In case of loss,

loss = cost price - selling price

selling price = cost price - loss

cost price = selling price + loss

3. Profit percentage and loss percentage

Profit percentage and loss percentage are always calculated on cost price unless otherwise stated.

In case of profit,

profit percentage=profit×100cost priceprofit percentage=profit×100cost price

selling price=cost price+cost price×profit percentage100=cost price(100+profit percentage)100selling price=cost price+cost price×profit percentage100=cost price(100+profit percentage)100

cost price=100×selling price100+profit percentagecost price=100×selling price100+profit percentage

Example: If an object is sold at a profit of 20%,20%,
selling price =120%=120% of cost price

In case of loss,

loss percentage=loss×100cost priceloss percentage=loss×100cost price

selling price=cost price−cost price×loss percentage100=cost price(100−loss percentage)100selling price=cost price−cost price×loss percentage100=cost price(100−loss percentage)100

cost price=100×selling price100−loss percentagecost price=100×selling price100−loss percentage

Example: If an object is sold at a loss of 20%20%
selling price =80%=80% of cost price

4. Selling at same price

(4.1) Suppose a person sells two objects at the same price, one at a profit of x1%x1% and another at a profit of x2%.x2%. Then,
net profit percentage =100(x1+x2)+2x1x2200+x1+x2=100(x1+x2)+2x1x2200+x1+x2
Note:
(a) for loss, use -sign for x1x1 and/or x2x2 as applicable.
(b) If the formula evaluates to a -ve value, it means there is a net loss

Example 1: Two objects are sold at the same price, one at a profit of 10%10% and another at a profit of 32%32%. Then,
100(10+32)+2×10×32200+10+32=20%100(10+32)+2×10×32200+10+32=20%
i.e., there is a net profit percentage of 20%20%

Example 2: Two objects are sold at the same price, one at a profit of 40%40% and another at a loss of 16%16%. Then,
100(40−16)+2×40×(−16)200+40−16=5%100(40−16)+2×40×(−16)200+40−16=5%
i.e., there is a net profit percentage of 5%5%

Example 3: Two objects are sold at the same price, one at a profit of 20%20% and another at a loss of 28%28%. Then,
100(20−28)+2×20×(−28)200+20−28=−10%100(20−28)+2×20×(−28)200+20−28=−10%
i.e., there is a net loss percentage of 10%10%

Example 4: Two objects are sold at the same price, one at a loss of 10%10% and another at a loss of 28%28%. Then,
100(−10−28)+2×(−10)×(−28)200−10−28=−20%100(−10−28)+2×(−10)×(−28)200−10−28=−20%
i.e., there is a net loss percentage of 20%20%

(4.2) Suppose a trader sells two objects at the same price, one at a profit of x%x% and another at a loss of x%.x%. Then he always incurs a net loss expressed as
net loss percentage =(x10)2=(x10)2

Example: Two objects are sold at the same price, one at a loss of 22%22% and another at a loss of 22%22%. Then,
net loss percentage =(2210)2=4.84%=(2210)2=4.84%