Maharashtra Board Class 8 Maths part 1 Chapter 9 Discount and Commission PDF Download

Discount And Commission

Let's Recall

Write the appropriate numbers in the following boxes.

1. \(\frac{12}{100}\) = Percent = __%

2. 47% = __

3. 86% = __

4. 4% of 300 = 300 × __ = __

5. 15% of 1700 = 1700 × __ = __

Let's Discuss

You may have seen such advertisements. In such a sale, a discount is offered on various goods. Generally in the month of July, sales of clothes are declared. Find and discuss the purpose of such sales.

Let's Learn

Discount

Mr. Suresh owns a saree shop. The details of sale of sarees and profit earned is given in the following table:

From the above table, it is clear that the discount is given on each saree during the sale in July. The profit on each saree is less but the total sarees sold are more. Hence overall there is more income for Mr. Suresh.

Teacher's Note

Discount means the shopkeeper reduces the price. In India, you see big discount sales in July and January when shops want to sell old clothes.

Exam Trick

Remember: Discount = Lower Price. Just like we get discounts on bus tickets during off-season, shops give discounts to sell more items.

Points to Remember

Discount is the amount reduced from the marked price.
Selling Price = Marked Price − Discount.
Discount is always given in percentage.
If marked price is Rs. 100 and 20% discount is given, then selling price is Rs. 80.

Each item to be sold has a price tag on it. The price on that tag is the 'Marked Price' of the item. Shopkeeper offers discount on the marked price. While selling the object, the actual amount by which he reduces the marked price is called the 'Discount'.

Hence the selling price = Marked Price − Discount.

Generally discount is given in terms of the percentage. A '20% discount' implies that an item should be sold by reducing the marked price by 20%. That is if the marked price of an item is Rs. 100 a discount of Rs. 20 is given on it. Hence the selling price of the item will be 100 − 20 = Rs. 80.

In such transaction if the discount is \(x\)%.

then \(\frac{x}{100} = \frac{\text{Discount}}{\text{Marked Price}}\)

\(\therefore \text{Discount} = \frac{\text{Marked Price} \times x}{100}\)

For More Information

At present, on line shopping of books, cloths, mobiles etc. is more popular than going to the market.

The companies which sell their goods online, do not have to spend much on shops and managements.

These companies not only give a discount but also give home delivery.

Solved Examples

Ex. (1) The marked price of a book is Rs. 360. The shop keeper sold it for Rs. 306. How much percent discount did the shopkeeper give?

Solution: Marked Price = ₹ 360, Selling Price = ₹ 306.

\(\therefore\) Discount = 360 − 306 = ₹ 54.

On marked price of Rs. 360, the discount is 54 rupees.

\(\therefore\) if the marked price is ₹ 100, let the discount be \(x\).

\(\frac{\text{Discount}}{\text{Marked price}} = \frac{x}{100}\)

\(\therefore \frac{54}{360} = \frac{x}{100}\)

\(\therefore x = \frac{54 \times 100}{360} = 15\)

\(\therefore\) 15% discount is given on the book.

Teacher's Note

To find discount percent, always compare the discount amount with the marked price. If a book costs Rs. 100 and you get Rs. 15 off, that is 15% discount.

Exam Trick

Remember: Discount percent = \(\frac{\text{Discount amount}}{\text{Marked Price}} \times 100\). Just like percentage in your exam marks.

Points to Remember

Discount is always calculated on marked price, not selling price.
Discount percent tells us how much price is reduced.
Formula: Discount = \(\frac{\text{Marked Price} \times \text{Discount percent}}{100}\).
Always check if discount is on marked price or cost price.

Ex. (2) The marked price of a chair is Rs. 1200. A 10% discount is given on it. Calculate the discount and selling price of the chair.

Solution: Method I

Marked price = ₹ 1200, discount = 10%

Let us find the ratio \(\frac{\text{discount}}{\text{marked price}}\)

Let us assume that, discount obtained is ₹ \(x\) on the marked price of a chair.

\(\therefore \frac{x}{1200} = \frac{10}{100}\)

\(x = \frac{10}{100} \times 1200\)

\(x = 120\)

Discount = ₹ 120.

Selling Price = Marked Price − Discount

= 1200 − 120

= 1080

Selling Price of a chair is ₹ 1080

Method II

10% discount is given on marked price. Therefore, if marked price is ₹ 100, then selling price is ₹ 90.

\(\therefore\) when marked price is 1200, let the selling price be ₹ \(x\).

\(\therefore \frac{x}{1200} = \frac{90}{100}\)

\(\therefore x = \frac{90}{100} \times 1200\)

\(\therefore x = 1080\)

Selling price of a chair is 1080 rupees.

\(\therefore\) discount = 1200 − 1080

= ₹ 120.

Ex. (3) After giving a discount of 20%, a saree is sold for Rs. 1120. Find the marked price of the saree.

Solution: Suppose, the marked price of the saree was Rs. 100. The discount given was 20%, therefore the customer got it for 100 − 20 = 80 rupees. That is, if the selling price was 80 rupees, the marked price was 100 rupees. Let us assume that the actual marked price of the saree, which was sold for Rs. 1120, was \(x\).

\(\therefore \frac{80}{100} = \frac{1120}{x}\)

\(\therefore x = \frac{1120 \times 100}{80} = 1400\)

\(\therefore\) marked price of the saree was 1400 rupees.

Teacher's Note

When you know selling price and discount percent, work backwards to find marked price. If an item is sold for Rs. 80 after 20% discount, the original price was Rs. 100.

Exam Trick

Remember: If discount is 20%, then customer pays 80% of marked price. Use this to find marked price from selling price.

Points to Remember

When discount is given, customer pays less than marked price.
If 20% discount is given, customer pays 80% of marked price.
Use ratio method: Selling Price / Marked Price = (100 − Discount%) / 100.
Always find marked price first, then calculate discount amount.

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