You might have seen while buying goods that on every article there is a price marked. This price is known as the market price (M.P.) of the article. In order to clear the stocks or to increase sale, sometimes shopkeepers offer a certain percent of rebate on the marked price for cash payments. This rebate is known as the discount. The customer or buyer pays the difference between the marked price and the discount.

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## Discount

Let us see the concept mathematically. Hence, we have: $$S.P.=\quad M.P.\quad –\quad Discount\quad in\quad Rs.$$

$$Rate\quad of\quad discount=discount\quad in\quad percentage\quad $$

$$discount\quad in\quad percentage=\frac { Discount }{ M.P. } \times 100$$

$$discount\quad in\quad percentage=\frac { M.P.-S.P. }{ M.P. } \times 100$$

As we know: $$S.P.=\quad M.P.\quad –\quad Discount\quad in\quad Rs.\\ S.P.\quad =\quad M.P.\quad -\frac { Discount\quad in\quad \%\quad \times M.P. }{ 100 } \\ S.P.\quad =\quad M.P.\left( 1-\frac { Discount\quad in\quad \% }{ 100 } \right) \\ S.P.\quad =\quad M.P.\left( \frac { 100-Discount\quad in\quad \% }{ 100 } \right) \\ M.P.\quad =\frac { S.P.\times 100 }{ 100-discount\quad in\quad \% } $$

Note: It should be noted that discount is given on the marked price only. Following examples will illustrate the computation of discount, selling price etc.

### Example 1

Find Selling Price of a toy if Market Price =Rs 650/- and Discount =10%

Solution: We have $$M.P.=Rs.650$$ and $$Discount\_ Rate = 10 \%$$

Therefore, $$Discount\quad in\quad Rs.=10 \%\quad of\quad Rs.650\\ Discount\quad in\quad Rs.\quad =Rs.\left( \frac { 10 }{ 100 } \times 650 \right) =Rs.65$$

Hence, $$S.P.=M.P. Discount\quad \\ S.P.=650Rs.-65Rs.\\ S.P.=585Rs.$$

### Example 2

Find the Market price of a chair, if Shalini paid Rs 3430 after discount of 2%.

Solution: As shalini paid Rs. 3430/- after discount of 2%. So $$S.P.=Rs.3430\\ Discount\_ Rate=2 \%$$

Therefore, $$M.P.\quad =\frac { S.P.\times 100 }{ 100-Discount\quad in\quad \% } $$

$$M.P.\quad =\frac { 3430\times 100 }{ 100-2 } Rs.\\ M.P.\quad =3500Rs.$$

### Example 3

Akshay paid Rs. 562.50 for T-shirt in a sale, while the price tag shows M.P. = Rs 625. Find discount in percentage.

Solution: We have, $$M.P.\quad =625Rs.\\ S.P.\quad =562.50Rs.$$

Therefore: $$Discount\quad in\quad Rs.=M.P.-S.P.\\ Discount\quad in\quad Rs=625Rs.-562.50Rs.\\ Discount\quad in\quad Rs=62.50Rs.$$

Hence, $$Discount\_ rate=\frac { Discount }{ M.P. } \times 100 \%\\ Discount\_ rate=\frac { 62.50Rs }{ 625Rs. } \times 100 \%\\ Discount\_ rate=10 \%$$

### Example 4

At a clearance sale, all goods are on sale at 45% discount. If I buy a skirt marked Rs 600, how much would I need to pay.

Solution: We have, $$M.P.=Rs600\\ Discount\_ Rate=45 /%$$

Therefore, $$S.P.\quad =\quad M.P.\left( \frac { 100-Discount\quad in\quad \% }{ 100 } \right) \\ S.P.\quad =600\left( \frac { 100-45 }{ 100 } \right) Rs.\\ S.P.=600\left( \frac { 55 }{ 100 } \right) Rs.\\ S.P.=330Rs.$$

## Commission

A commission is paid to the salesperson for his/her services by the seller with respect to the M.P. For example, if Radhika is a salesperson and works in a garment shop and takes 2% commission. It means from shop owner Radhika take 2Rs for selling of 100Rs (M.P.). In this case, the shop owner is sharing his revenue, thus his profit is reduced. Types of commission:

- Standard commission
- Base wage plus commission
- Graduate or tiered commission

### Example 1

Norman earns 6% commission on each baseball uniform he sells. If each uniform cost RS 90 and he sells 21 uniforms to the baseball team. How much commission will Norman earn?

**Solution: **Given: $$Commission\quad rate\quad =\quad 6%\\ No\quad of\quad sales\quad =\quad 21\\ cost\quad of\quad 1\quad uniform\quad =90rs.$$. Thus, $$revenue=21\times 90Rs.\\ revenue=1890Rs.$$ and Commission earned by Narman: $$Commission\quad =\quad \frac { Commission\quad rate\times revenue }{ 100 } \\ Commission\quad =\quad \frac { 6\times 1890 }{ 100 } Rs.\\ \\ Commission\quad =113.40Rs$$

## More Solved Examples For You

Q1. After allowing a discount of 12% on the marked price of an article, it is sold for Rs 880. Find the market price.

Answer: We have, $$S.P.=Rs880\\ Discount\_ rate=12 \%$$ . Therefore, $$M.P.\quad =\frac { S.P.\times 100 }{ 100-discount\quad in\quad \% } \\ M.P.\quad =\frac { 880\times 100 }{ 100-12 } Rs.\\ M.P.\quad =\frac { 880\times 100 }{ 88 } Rs.\\ M.P.\quad =1000Rs.$$

Q2. A shopkeeper offers his customers 10% discount and still makes a profit of 26%. What is the actual cost to him of an article marked Rs 280.

Answer: Shopkeeper makes proa fit of 26% on selling price item. First, we will determine the selling price of the item.

#### Calculation of selling price

We know: $$M.P.=Rs280\\ Discount\_ Rate=10%$$ . Therefore, $$S.P.\quad =\quad M.P.\left( \frac { 100-discount\quad in\quad % }{ 100 } \right) \\ S.P.\quad =\quad 280\left( \frac { 100-10 }{ 100 } \right) Rs.\\ S.P.\quad =\quad 280\left( \frac { 90 }{ 100 } \right) Rs.\\ S.P.\quad =\quad 252Rs.$$

#### Calculation of cost price

Now we that $$S.P.\quad =\quad 252Rs.\\ Gain=26 \%$$ , Therefore, $$C.P.\quad =\quad S.P.\left( \frac { 100 }{ 100+Gain\quad \% } \right) \\ C.P.\quad =\quad 252\left( \frac { 100 }{ 100+26 } \right) Rs.\\ C.P.\quad =\quad 252\left( \frac { 100 }{ 126 } \right) Rs.\\ C.P.\quad =\quad 200Rs.$$

Hence, the actual cost of the article is Rs 200

** Question.** What is the way of calculating a discount?

**Answer.** In order to calculate a discount, one must multiply the original price by the decimal form of the percentage. In order to calculate the item’s sale price, subtract the discount from the original price. One can do this by using a calculator or manual estimation.

**Question.** How can one take 20% off a price?

**Answer.** First of all, one must convert the percentage discount to a decimal. So, a 20 per cent discount happens to be 0.20 in decimal format. Secondly, one must multiply the decimal discount by the item’s price to determine the savings in dollars.

**Question.** Explain what is a discount with example?

**Answer.** Discount refers to reduced prices or something sold at a price that is lower than the normal price. For example, a purse sold for 50 per cent off its normal price or a store that sells designer items at prices that are below market price.

**Question.** Explain how one can calculate a 10% discount?

**Answer.** The simple way of calculating 10% discount is to first divide the total sale price by 10. This should be followed by subtraction from the price.