# Class-8 Tax and Discount

Introduction to Tax and Discount

## Introduction to Tax and Discount

Shopkeepers sometimes offer goods at reduced prices in order to dispose off old or damaged goods or to increase the sales or to attract customers to buy their products.

* Discount* means reduction in prices.

## Marked Price

The price printed on an article or written on a slip attached to every items are called its marked price and it is written as **M.P**. The marked price of an article is also called listed price.

## Listed Price

Items which are manufactured in a factory are marked with a price according to the list supplied by the factory, where retailer is needed to sell them. This price is known as the list price of the article.

## Discount

The amount deducted from the marked price of an article is called discount or otherwise it is called trade discount. Discount is always given on the marked price of article as percentage. For example − Usually we say by discount of 15%. It means that price of the article is to be reduced by 15% of the marked price.

## Selling Price

The price of an article after deducting discount from the marked price is called its selling price. This price of article paid by customer.

*Selling Price = Marked Price − Discount*

For solving problems on discount, we should remember following points.

- Discount is always given on the marked price
- Selling price = Marked Price − Discount
- Discount Percentage = (
^{Discount}⁄_{Marked Price}) × 100 - If the discount is D%, then S.P = M.P − Discount = M.P − D% of M.P
- If two successive discounts are D1 % and D2 %, then

*S.P = {*^{(1−D1)}⁄_{100}} × {^{(1−D2)}⁄_{100}} × M.PLet's see some examples to understand it better.

**Example 1.** A crockery set is marked at Rs. 2500. The big mart offers 20% discount on it. Find the discount and net price that customer pays.

**Solution.** Here, Marked Price = Rs.2500.

Discount= 20%

Amount of discount = 20% of Rs. 2500 = {(^{20}⁄_{100}) × 2500} = Rs. 500

Net sale price the customer pays = Marked Price − Amount of discount

= (2500 − 500)

= Rs. 2000

Hence, the customer pays Rs. 2000.

**Example 2.** Marked price of item is Rs. 600 and it sold for Rs. 520. What is the discount and discount %?

**Solution.** Marked Price (M.P) of the item = Rs. 600

Selling price (S.P) of the item = Rs. 520

Discount = M.P − S.P = (600 − 520) = Rs. 80

Discount % = {(^{Discount}⁄_{M.P}) × 100}%

= {(^{80}⁄_{600}) × 100}%

= (^{40}⁄_{3})%

= 13.33%

**Example 3.** A dining table is sold at Rs. 5700 after giving a discount of 5%.Find its marked price.

**Solution.** Let's assume marked price of dining table is P.

S.P of dining table = Rs. 5700, discount = 5%

Discount amount = 5% of P = {(^{5}⁄_{100}) × P} = ^{P}⁄_{20}

As we know, S.P = M.P − Discount

5700 = P − ^{P}⁄_{20}

=> 5700 = ^{19P}⁄_{20}

=> P = ^{(5700×20)}⁄_{19}

=> P = Rs. 6000

Hence, the marked price of dining table is Rs. 6000.

**Example 4.** A trader marks his goods 30% above cost price and allows a discount of 15%. What gain percent does he make?

**Solution.** Let's assume cost price = P

M.P = (P + 50% of P) = P + (^{50P}⁄_{100})= (^{3P}⁄_{2})

S.P = M.P − Discount = {(^{3P}⁄_{2}) − (20% of ^{3P}⁄_{2})}

= {(^{3P}⁄_{2}) − (^{20}⁄_{100} × ^{3P}⁄_{2})

= {^{3P}⁄_{2}) − ^{3P}⁄_{10})}

= ^{6P}⁄_{5}

Gain = S.P − C.P = ^{6P}⁄_{5} − P = ^{P}⁄_{5}

Gain% = {[(^{P}⁄_{5}) ÷ P] × 100}% = 20%.

**Example 5.** A Retailer purchased a sewing machine for Rs. 1500. He sells it at a discount of 25% and still makes a profit of 5%. Find the selling price and the marked price.

**Solution.** C.P = Rs. 1500, profit = 5%

As we know, S.P = (1 + ^{P}⁄_{100}) of M.P (Where P = Profit)

S.P = (1 + ^{5}⁄_{100}) of 1500 = (^{105}⁄_{100}) × 1500 = Rs. 1575
Hence, selling price is Rs. 1575

Now, S.P = Rs. 1575, discount 25%

According to formlua S.P. = (1 − ^{25}⁄_{100}) of M.P

=> 1575 = ^{75}⁄_{100} × M.P

=> M.P = ^{1575}⁄_{75} × 100

=> M.P = Rs. 2100

Hence, Marked price is Rs. 2100.

**Example 6.** A shopkeeper purchased a bicycle at 10% discount on the marked price but sold it at the marked price. Find his profit percentage.

**Solution.** Let's the marked price of the bicycle is 'M' rupees.

Shopkeeper purchased a bicycle at 10% discount.

Here, C.P = M.P − 10% of M.P

= M − ^{10}⁄_{100} of M

= M − ^{M}⁄_{10}

= ^{9M}⁄_{10}

As bicycle is sold at the marked price, S.P = M

Profit = S.P − C.P = M − ^{9M}⁄_{10} = ^{M}⁄_{10}

Profit percentage = {[(^{M}⁄_{10}) ÷ (^{9M}⁄_{10})] × 100}%

= 11.11%

**Example 7.** A retailer marks his product 30% above the cost price and allows a discount of 10%. Find his profit percentage.

**Solution.** Let the cost price of the product is 'P'.

Since the retailer marks the product 30% above the cost price, then

Then marked price (M.P) = C.P + 30% of C.P

= P + 30% of P

= p + ^{30P}⁄_{100}

= P + ^{3P}⁄_{10}

= ^{13P}⁄_{10}

As we know S.P. = (1 − ^{10}⁄_{100}) of M.P

= {1 − (^{1}⁄_{10})} of ^{13P}⁄_{10}

= ^{9}⁄_{10} × ^{13P}⁄_{10}

= ^{117P}⁄_{100}

Profit = S.P − C.P = ^{117P}⁄_{100} − P

= ^{(117P − 100P)}⁄_{100}

= ^{17P}⁄_{100}

Profit Percentage = {[(^{17P}⁄_{100}) ÷ P] × 100}%

= 17%

**Example 8.** The marked price of Refrigerator is Rs. 2600. A shopkeeper allows two successive discount of 10% and 5%. Find the price which a customer has to pay for the Refrigerator.

**Solution.** Here, M.P = 2600, D1 = 10%, D2=5%

The selling price of Refrigerator

S.P = (1 − ^{D1}⁄_{100})(1 − ^{D2}⁄_{100}) of M.P

= (1 − ^{10}⁄_{100})(1 − ^{5}⁄_{100}) × 2600

= Rs. 2223

Hence, the customer has to pay Rs. 2,223 for refrigerator.

**Example 9.** Find the single discount equivalent to two successive discounts of 35% and 7%

**Solution.** Let the marked price of an article be rupees M and a single discount of D% be equivalent to two given successive discounts of 35% and 7%.

Here, selling price of both must be equal.

(1 − ^{D}⁄_{100}) of M = (1 − ^{35}⁄_{100})(1 − ^{7}⁄_{100}) of M

=> 1 − ^{D}⁄_{100} = ^{65}⁄_{100} × ^{93}⁄_{100}

=> 100 − D = ^{65}⁄_{100} × ^{93}⁄_{100} × 100

=> 100 − D = 60.45

=> D = 100 − 60.45

=> D = 39.55

Hence, a single discount of 39.55 is equivalent to two given successive discounts.

## Goods and Service Tax

A compulsory contribution to generate revenues, imposed by central government and state government added to the cost of good and services is known as Tax.

**G**ood and **S**ervices **T**ax (GST) is charged by the state government on the item to be sold. GST is collected by shopkeeper from the customer and given to the central and state government.

## GST Calculation Procedure

GST is calculated on the selling price of a product and is added to the bill. For any discounted items, first discount should be deducted given by the shopkeeper from marked price and then calculate GST on selling price.

Let's see some examples to understand the calculation.

**Example 1.** The cost of a shirt at a shop was Rs. 650. The goods and services tax charged was 8%. Find the bill amount.

**Solution.** Cost of a shirt = Rs. 650

GST = 8% of 650 = (^{8}⁄_{100}) × 650 = Rs. 52

Bill Amount = cost of item + GST

= 650 + 52

= Rs. 702

Hence, bill amount is equal to Rs. 702

**Example 2.** Shreya purchased a hair straightening iron rod for Rs. 8100 including 8% GST. Find the price before GST was added.

**Solution.** Let the original price of the hair straightening before GST be P rupees.

GST = 8% of P = (^{8}⁄_{100}) × P = ^{2P}⁄_{25}

Price including GST = (P + ^{2P}⁄_{25}) = ^{27P}⁄_{25}

Hence, ^{27P}⁄_{25} = 8100

=> P = 8100 × ^{25}⁄_{27}

=> P = Rs. 7500

Hence, the price of the hair straightening iron rod before GST is equal to Rs. 7500.

**Example 3.** The marked price of an ipad is Rs. 7500. The shopkeeper gives a discount of 7% on cash payment. If the GST is 8%, find the amount the customer has to pay while purchasing the ipad.

**Solution.** Marked price of ipad = Rs. 7500

Rate of discount = 7%

Discount = 7% of 7500

= ^{7}⁄_{100} × 7500

= Rs. 525

S.P of ipad = M.P − discount

= 7500 − 525

= Rs. 6975

Now GST = 8% of 6975

= ^{8}⁄_{100} × 6975

= Rs. 558

Bill amount = Rs. 6975 + Rs. 558

= Rs. 7533

Hence, the customer has to pay Rs. 7533 to purchase iPad.

**Example 4.** Anuja wants to purchase a Television whose marked price is Rs. 37800 excluding 8% GST. But she has Rs. 37800 only, she requests the shopkeeper to reduce the price of Television in such way that she has to pay Rs. 37800 including GST. Find the amount reduced by the shopkeeper.

**Solution.** Let the reduced price of Television be rupees 'M'.

GST = 8% of rupees M = (^{8}⁄_{100}) × M = ^{2M}⁄_{25}

Amount paid by Anuja = M + ^{2M}⁄_{25} = ^{27M}⁄_{25}

As Anuja has Rs. 37800 to purchase Television, then

=> ^{27M}⁄_{25} = 37800

=> M = ^{(37800×25)}⁄_{27}

=> M = 35000

Amount reduced = 37800 − 35000 = Rs. 2800

Hence, the amount reduced by the shopkeeper is Rs. 2800.

## Class-8 Tax and Discount Worksheets

Tax and Discount Worksheet - 1

Tax and Discount Worksheet - 2

## Answer Sheet

**Tax-Discount-Answer**Download the pdf

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