## Definitions

Sometimes to increase the sale or to dispose off the old stock, a dealer offers his goods at reduced prices. The reduction in price offered by the dealer is called discount.

Marked Price: The printed price or the tagged price of an article is called the marked price (M.P.). It is also called the list price.

Discount: The deduction allowed on the marked price is called discount. Discount is generally given as per cent of the marked price.

Net Price: The selling price at which the article is sold to the customer after deducting the discount from the marked price is called the net price.

## Formulas

(i) S.P. = M.P. – Discount

(ii) Rate of discount = Discount % =  $$\frac{Discount}{M.P.}$$ x 100

(iii) S.P. = M.P. x ($$\frac{100 – Discount \%}{100}$$)

(iv) M.P. = $$\frac{100 * S.P.}{100 – Discount \%}$$

## Illustrative Examples

Example 1: Find S.P. if M.P. = Rs 650 and Discount = 10%

Solution. (i) We have,

M.P. = Rs 650, Discount = 10%

Discount = 10% of Rs 650 = Rs($$\frac{10}{100}$$ x 650) = Rs 65

Hence, S.P. = M.P. — Discount = Rs 650 — Rs 65 = Rs 585

Alternative Solution–    We have,

M . P. = Rs 650, Discount % =10

S.P. = M.P. x $$\frac{(100 – Discount \%)}{100}$$

=>    S.P. = Rs {650 x $$\frac{(100 -10)}{100}$$} = Rs(65 x 9) = Rs 585

Example 2: Find the rate of discount when M.P. = Rs 600 and S.P. = Rs 510.

Solution.    M.P. = Rs 600, S.P. = Rs 510

Therefore,    Discount = M.P. — S.P. = Rs 600 — Rs 5l0 = Rs 90

Therefore,    Rate of discount, i.e., discount% = $$\frac{Discount}{M.P.}$$ x 100 = $$\frac{90}{600}$$ x 100% = 15%.

Example 3: Find the M.P. When S.P. = Rs 9,000 and discount = 10%.

Solution.    S.P. = 9000, discount = 10%
Let the M.P. be Rs 100. Since discount = 10%, So S.P. = Rs 90.

When S.P. is 90, M.P. is 100.

When S.P. is Rs 1, M.P. is Rs $$\frac{100}{90}$$
When S.P. is Rs 9000, M.P. is Rs $$\frac{100}{90}$$ x 9000 = Rs 10,000

Example 4: A garment dealer allows his customers 10% discount on a marked price of the goods and still g a profit of 25%. What is the cost price if the marked price of a shirt is Rs 1250?

Solution.    M.P. = 1250, Discount = 10%

When M.P. is 100, S.P. is 90

When M.P. is 1250, S.P. is Rs $$\frac{900}{100}$$ = Rs 1125

Profit = 25%, So C.P. = $$\frac{100}{(100 + Profit \%)}$$ x S.P.
= Rs $$\frac{100}{(100 + 25)}$$ x 1125

= Rs $$\frac{100}{125}$$ x 1125
= Rs(100 x 9) = Rs 900

Successive Discounts

Example 5: A car is marked at 4,00,000. The dealer allows successive discounts of 5%, 3% and $$2\frac{1}{2}$$% on it. What is the net selling price ?

Solution.    Marked price of the car = Rs 4,00,000

First discount = 5% of 4,00,000 = ($$\frac{5}{100}$$ x 400000) = Rs 20,000

Net price after first discount = (4,00,000 — 20,000) = 3,80,000

Second discount = 3% of Rs 3,80,000 = ($$\frac{3}{100}$$ x 380000) = Rs 11,400

Net price after second discount = (3,80,000 — 11,400) = Rs 3,68,600

Third discount = Rs ( $$\frac { 2\frac { 1 }{ 2 } }{ 100 }$$ x 3, 68, 600)
= ($$\frac{5}{200}$$ x 368600) = Rs 9215

Net selling price = Rs (3,68,600 — 9215) = Rs 3,59,385.

Example 6: Find a single discount equivalent to two successive discounts of 20% and 5%.

Solution.    Let the marked price be Rs 100.

First discount = Rs 20

Net price after first discount = Rs (100 — 20) = Rs 80

Second discount 5% of Rs 80 = Rs ($$\frac{5}{100}$$ x 8O) = Rs 4

Net price after second discount = Rs (80 — 4) = Rs 76

Total discount allowed = Rs (100 — 76) = Rs 24

Hence, the required single discount = 24%.