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%.