ICSE Class 10 Maths Chapter 01 Value Added Tax

Unit 1: Commercial Mathematics

Value Added Tax

Introduction

The government of every state and the government at centre need money:

(i) to meet their administrative expenses,

(ii) to execute their welfare and development schemes,

(iii) to meet the expenses on salaries of their employees, etc.

In order to collect money (revenue), different state governments levy tax on the sale of goods within their respective territories. This tax is known as Sales Tax or Trade Tax. For the movement of goods from one state to another, the Union Government also levies Sales Tax, known as Central Sales Tax (C.S.T.).

Some Important Terms

Cost (basic) Price (C.P.): It is the price at which a trader buys goods. The cost price is also termed basic price.

Selling Price (S.P.): It is the price at which a trader sells his goods (without including any tax). Selling-price is also called sale-price.

Profit or Loss: (i) Profit = S.P. - C.P. and Loss = C.P. - S.P.

(ii) Profit% = \(\frac{\text{Profit}}{\text{C.P.}}\) \(\times\) 100% and Loss% = \(\frac{\text{Loss}}{\text{C.P.}}\) \(\times\) 100%

List Price: It is the price at which the article is marked. List price is also known as marked price (M.P.), printed price, quoted price, etc.

Discount: In order to sell out the old stock or for some other reason(s), shopkeepers give certain percentage of the list price as discount. This discount is always calculated on list price / marked price.

When an article is sold without any discount, its sale-price = its M.P.

Computation of Sales Tax

The calculation of Sales Tax is very easy as it involves very simple concepts of percentage.

The rates of Sales Tax depend upon the nature of goods purchased and are different for different goods (items). Different states have different rates of Sales Tax even on the same items (goods). Some items of necessity and / or of daily use for common people are completely or partially exempted from Sales Tax.

Sales Tax is calculated on the Sale Price.

Sales Tax = \(\frac{\text{Rate of Sales Tax} \times \text{Sale Price}}{100}\)

Rate of Sales Tax = \(\frac{\text{Sales Tax}}{\text{Sale Price}}\) \(\times\) 100%

If the rate of Sales-Tax is x%, then price paid for the item = Its sale-price \(\times\) \(\left(\frac{100+x}{100}\right)\)

The amount of money paid by a customer for an article = The Sale Price of the article + Sales Tax on it, if any.

Example 1

Rohit purchased a pair of shoes costing \(\text{₹}\) 850. Calculate the total amount to be paid by him, if the rate of Sales Tax is 6%.

Solution:

Sale price of shoes = \(\text{₹}\) 850

and, Sales Tax = 6% of \(\text{₹}\) 850 = \(\text{₹}\) 51

Therefore, Total amount to be paid by Rohit = \(\text{₹}\) 850 + \(\text{₹}\) 51 = \(\text{₹}\) 901

Direct method:

Amount paid by Rohit = \(\text{₹}\) 850 \(\left(\frac{100+6}{100}\right)\) = \(\text{₹}\) 901

Example 2

Mr. Gupta purchased an article for \(\text{₹}\) 702 including Sales Tax. If the rate of Sales Tax is 8%, find the sale price of the article.

Solution:

Let the sale price of the article be \(\text{₹}\) x

Therefore, x + 8% of x = \(\text{₹}\) 702

x = \(\text{₹}\) 702 \(\times\) \(\frac{100}{108}\) = \(\text{₹}\) 650

Therefore, Sale price of the article = \(\text{₹}\) 650

Direct method:

\(\text{₹}\) 702 = Sale-price \(\left(\frac{100+8}{100}\right)\)

\(\text{₹}\) 702 \(\times\) \(\frac{100}{108}\) = Sale-price

Sale-price = \(\text{₹}\) 650

Example 3

Geeta purchased a face-cream for \(\text{₹}\) 79.10 including Sales Tax. If the printed price of the face-cream is \(\text{₹}\) 70, find the rate of Sales Tax.

Solution:

Total price (including Sales Tax) = \(\text{₹}\) 79.10 and, printed price = \(\text{₹}\) 70

Therefore, Sales Tax paid = \(\text{₹}\) 79.10 - \(\text{₹}\) 70 = \(\text{₹}\) 9.10

and, the rate of Sales Tax = \(\frac{9.10}{70}\) \(\times\) 100% = 13%

Example 4

Mrs. Sharma purchased confectionery goods costing \(\text{₹}\) 165 on which the rate of Sales Tax is 6% and some tooth-paste, shaving-cream, soap, etc., costing \(\text{₹}\) 230 on which the rate of Sales Tax is 10%. If she gives a five-hundred rupee note to the shopkeeper, what money will he return to Mrs. Sharma?

Solution:

Price of confectionery goods including Sales Tax = \(\text{₹}\) 165 + 6% of \(\text{₹}\) 165 = \(\text{₹}\) 174.90

Price of tooth-paste, shaving-cream, soap, etc. including Sales Tax = \(\text{₹}\) 230 + 10% of \(\text{₹}\) 230 = \(\text{₹}\) 253

Therefore, Total amount to be paid by Mrs. Sharma = \(\text{₹}\) 174.90 + \(\text{₹}\) 253 = \(\text{₹}\) 427.90

Since Mrs. Sharma gave a five-hundred rupee note to the shopkeeper, the money that the shopkeeper will return to Mrs. Sharma = \(\text{₹}\) 500 - \(\text{₹}\) 427.90 = \(\text{₹}\) 72.10

Teacher's Note

Sales Tax is a practical example of percentage application in everyday shopping. When you buy anything, the final amount you pay includes the base price plus the tax.

Problems Involving Overhead Charges and Discounts

Example 5

A trader from Meerut buys an article for \(\text{₹}\) 3,600 (inclusive of all taxes) from Kanpur. He spends \(\text{₹}\) 1,200 on travelling, transportation of the article, etc. If he desires a profit of 15 percent, how much will a customer pay for the article? The rate of Sales Tax paid by the customer is 8%.

Solution:

For the trader:

Price paid for the article = \(\text{₹}\) 3,600

Overheads = \(\text{₹}\) 1,200

Therefore, Cost price of the article = \(\text{₹}\) 3,600 + \(\text{₹}\) 1,200 = \(\text{₹}\) 4,800

And, sale-price = \(\left(\frac{100+15}{100}\right)\) of \(\text{₹}\) 4,800 (As, profit desired = 15%)

= \(\frac{115}{100}\) \(\times\) \(\text{₹}\) 4,800 = \(\text{₹}\) 5,520

Therefore, Money paid by the customer = Sale-price of the article + Sales Tax on it

= \(\text{₹}\) 5,520 + 8% of \(\text{₹}\) 5,520 = \(\text{₹}\) 5,961.60

Example 6

A shopkeeper buys an article for \(\text{₹}\) 1,500 and spends 20% of the cost on its packing, transportation, etc. Then he marks the article at a certain price. If he sells the article for \(\text{₹}\) 2,452.50 including 9% Sales Tax on the price marked, find his profit as percent.

Solution:

Let marked price of the article be \(\text{₹}\) x

Therefore, \(\text{₹}\) x + \(\text{₹}\) \(\frac{9x}{100}\) = \(\text{₹}\) 2,452.50 (Therefore Sales-tax = 9%)

On solving, we get: x = 2,250

Therefore, Marked price of the article = \(\text{₹}\) 2,250 = Its selling price

Since, the shopkeeper buys the article for \(\text{₹}\) 1,500 and spends 20% of the cost as overheads,

Therefore, Total cost price of the article = \(\text{₹}\) 1,500 + 20% of \(\text{₹}\) 1,500 = \(\text{₹}\) 1,500 + \(\text{₹}\) 300 = \(\text{₹}\) 1,800

Profit = Selling price - Total cost price = \(\text{₹}\) 2,250 - \(\text{₹}\) 1,800 = \(\text{₹}\) 450

Profit % = \(\frac{\text{₹}\,450}{\text{₹}\,1800}\) \(\times\) 100% = 25%

Example 7

The catalogue price of a computer set is \(\text{₹}\) 45,000. The shopkeeper gives a discount of 7% on the listed price. He gives a further off-season discount of 4% on the balance. However, Sales Tax at 8% is charged on the remaining amount. Find:

(i) the amount of Sales Tax a customer has to pay,

(ii) the final price he has to pay for the computer set.

Solution:

Since, the list price = \(\text{₹}\) 45,000

Discount = 7% of \(\text{₹}\) 45,000 = \(\text{₹}\) 3,150

Therefore, Price after discount = List price - Discount = \(\text{₹}\) 45,000 - \(\text{₹}\) 3,150 = \(\text{₹}\) 41,850

Off-season discount = 4% of \(\text{₹}\) 41,850 = \(\text{₹}\) 1,674

Therefore, Sale-price = \(\text{₹}\) 41,850 - \(\text{₹}\) 1,674 = \(\text{₹}\) 40,176

(i) The amount of Sales Tax a customer has to pay = 8% of \(\text{₹}\) 40,176 = \(\text{₹}\) 3,214.08

(ii) The final price, the customer has to pay for the computer = Sale-price + Sales Tax = \(\text{₹}\) 40,176 + \(\text{₹}\) 3,214.08 = \(\text{₹}\) 43,390.08

Example 8

Dinesh bought an article for \(\text{₹}\) 374, which included a discount of 15% on the marked price and a sales-tax of 10% on the reduced price. Find the marked price of the article.

Solution:

Let the marked price be \(\text{₹}\) 100

Therefore, Discount = 15% of \(\text{₹}\) 100 = \(\text{₹}\) 15

Therefore, Sale-price = \(\text{₹}\) 100 - \(\text{₹}\) 15 = \(\text{₹}\) 85

Sales-tax = 10% of \(\text{₹}\) 85 = \(\text{₹}\) 8.50

Therefore, Price paid by Dinesh for the article = \(\text{₹}\) 85 + \(\text{₹}\) 8.50 = \(\text{₹}\) 93.50

When Dinesh paid = \(\text{₹}\) 93.50, M.P. = \(\text{₹}\) 100

Therefore, When Dinesh paid = \(\text{₹}\) 1, M.P. = \(\text{₹}\) \(\frac{100}{93.50}\)

Therefore, When Dinesh paid = \(\text{₹}\) 374, M.P. = \(\text{₹}\) \(\frac{100}{93.50}\) \(\times\) 374 = \(\text{₹}\) 400

Alternative method:

Let the marked price of the article be \(\text{₹}\) x

Therefore, Discount = 15% of \(\text{₹}\) x = \(\text{₹}\) \(\frac{15}{100}\) \(\times\) x = \(\text{₹}\) \(\frac{3x}{20}\)

Therefore, Sale-price = \(\text{₹}\) x - \(\text{₹}\) \(\frac{3x}{20}\) = \(\text{₹}\) \(\frac{17x}{20}\)

Therefore, Price paid by Dinesh = \(\left(\frac{100+10}{100}\right)\) \(\times\) \(\frac{17x}{20}\) = \(\text{₹}\) \(\frac{187x}{200}\) (Therefore Sales-tax = 10%)

Given: \(\frac{187x}{200}\) = 374 => x = 374 \(\times\) \(\frac{200}{187}\) = 400

Therefore, Marked price = \(\text{₹}\) 400

Direct method:

Since, discount = 15% and sales-tax = 10%

Price-paid = Marked price \(\times\) \(\left(\frac{100-15}{100}\right)\) \(\times\) \(\left(\frac{100+10}{100}\right)\)

=> \(\text{₹}\) 374 = M.P. \(\times\) \(\frac{85}{100}\) \(\times\) \(\frac{110}{100}\)

=> M.P. = \(\text{₹}\) 374 \(\times\) \(\frac{100}{85}\) \(\times\) \(\frac{100}{110}\) = \(\text{₹}\) 400

Teacher's Note

When buying electronics or appliances, stores often advertise discounts on marked price before adding sales tax, which is why the final bill is often higher than the advertised sale price.

This is a preview of the first 3 pages. To get the complete book, click below.