Page 111 - ICSE Math 8

10 Profit, Loss, Discount and Tax

Key Concepts

• Profit and Loss, Overhead Expenses • Discount
• Profit% and Loss% • Tax

You must have seen people asking for discounts from shopkeepers. On some products, the shopkeepers willingly
give a discount while on some they completely refuse. Let us see the factors and terms which effect the cost
of an article and the discount given on it.
Cost Price (C.P.): The price/amount paid to buy an article is called its cost price (C.P.).
Overhead Expenses: The expenses incurred in packing, cartage, taxes, labour charges, etc., are called overhead
expenses. These are normally included in the cost price. If not, they are added to the cost price.

Effective C.P. = C.P. + Overhead expenses
Selling Price (S.P.): The price/amount at which an article is sold is called its Maths Info
selling price (S.P.).
Loss or Gain is always calculated
Profit: The gain made if the S.P. is more than the C.P. is called profit. on the cost price.
Profit = S.P. – C.P.
Profit Per cent: The profit per cent is the profit made on the C.P., if the C.P. is ` 100.

Profit 1  00 Profit%  100 S.P.×
+
Profit% = × 100 S.P. =   × C.P. C.P. =
C.P.  100  (100 + Profit%)
Loss: If the S.P. of an article is less than its C.P., then the difference between the C.P. and the S.P. is called loss.
Loss = C.P. – S.P.

Loss Per cent: The loss per cent is the loss made on the C.P., if the C.P. is ` 100.

Loss Ê 100 - Loss% ˆ 100 ¥S.P.
Loss% = ×100 S.P. = Á ˜ ¥ C.P. C.P. =
C.P. Ë 100 ¯ ( 100 - Loss%)

Example 1: Sangeeta bought a computer for ` 25,650. Due to some defect in it, she had to pay ` 1,350 for
its repair. Then she sold it for ` 28,700. Find her gain or loss per cent.
Solution: C.P. of the computer = ` 25,650
Amount spent on its repair = ` 1,350
∴ Total investment (new C.P.) = ` (25,650 + 1,350) = ` 27,000
S.P. of the computer = ` 28,700
Since S.P. > C.P, there is a gain.

Gain = S.P. – C.P. = ` (28,700 – 27,000) = ` 1,700

Ê Gain ˆ Ê 1 700, ˆ
Gain% = Á C.P. ¥100 % = Á Ë 27 000, ¥100 % = 6.29%
˜
˜
¯
Ë
¯
Hence, Sangeeta made a profit of 6.29%.
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