Profit and loss

Amrit bought an article for Rs. 2,200 and sold it for Rs. 2,500. Here, his selling price is greater than the cost price. Hence, he got a profit of Rs. 2,500 - Rs. 2,200 = Rs. 300. If he had sold the article for Rs. 2000, he would have a loss of Rs. 2,200 - Rs. 2,000 = Rs. 200. The price for which an article is bought is known as the cost price (C.P.). The price for which it is sold is known as selling price (S.P.). If the selling price is greater than cost price, there is profit or gain. On the other hand, if the selling price is less than the cost price, there is a loss.

So, Profit = Selling price (S.P) - Cost price (C.P)
P = SP - CP and Loss =Cost price (C.P) -Selling price (S.P)
L = CP - SP

The percentage profit or loss can be calculated using the following formula.

Actual profit = profit% of cost price

\(\text {Profit percentage} = \frac {Profit} {C.P}\times 100\)

Actual loss = loss% of Cost price.

\(\text {Loss percentage} = \frac {Loss} {C.P}\times 100\)

If S.P and profit or loss percent are given then

\(C.P = \frac {S.P \times 100} {100 + P\%} \: {or}\: C.P = \frac {S.P \times 100} {100 - L\%}\)

If C.P. and profit or loss percentage are given then

\(S.P = \frac {C.P \times (100 + P\%)} {100}\: {or}\: S.P = \frac {C.P \times (100 - L\%)} {100}\)

Discount

The seller may deduct a certain amount from the price of goods. The deduction is known as discount. The price from which the discount is deducted is called the marked price or labeled price. The price obtained by deducting the discount from marked price is called selling price
i.e. Selling price (S.P) = Market price (M.P) - Discount
S.P = M.P - D
or, M.P = S.P + D
or, D = M.P - S.P

If there is no discount, selling price = marked price [ S.P = M.P ]

\(\text {Discount percentage} = \frac {Discount} {M.P} ×100%\)

Value Added Tax (VAT)

Value Added Tax is a tax imposed by the government based on goods and services in each step of production and distribution. VAT is levied in the amount after allowing the discount (if there is) from the market price. In general, VAT is expressed in terms percentage which is called the rate of the VAT and it is fixed by the government. The cost of goods is determined by adding the VAT.

S.P = Orginal cost + VAT

\(\text {Rate of VAT} = \frac {VAT \;Amount} {Cost \; after \; discount (S.P)} \times 100\%\)

VAT amount = Rate of VAT (in%) \(\times\) discounted price.