Subject: Compulsory Maths

The amount paid by a company or manufacturer at the certain rate for the service or the sale of the certain type of item in certain quantity is called commission. Commission, in general, is expressed in percentage(%). A person, organization, industry or company the amount at a fixed rate or certain criteria to the government or the government institution for the earning of capital that amount paid is called a tax.

Commission is paid by the company at a certain rate for the agent at selling the service. Commission is expressed in terms of percentage(%). As the business increases the commission also increases.

A company related to selling and purchasing of land in Biratnagar receives 5% of the selling price from the land owner after arranging the selling of the land.

A foreign motor car company provides the following amount on sales to its company authorized agent or dealer for the purpose of the promotion of the sale at the following rate:

4% on the annual sale up to Rs. 4000000.

5% on the annual sale up to Rs. 5500000.

7% on the annual sale to Rs. 10000000.

But the same company provides 5.5% of the total sale to the sales person of a jeep. Therefore, the amount received by the sales person on the sale of the jeep for Rs. 5500000.

While solving the problems relating to commission, following formulae are used:

- Commission = fixed percentage of selling price
- Price after commission = selling price - commission amount
- Commission % = \(\frac {commission}{selling\;price}\)×100 %

A person, organization, industry or company pays the amount at a fixed rate or under certain criteria to the government or the government institutions (like VDC, municipality, metropolitan, tax office) for the earning of capital. The money so paid is called a tax. There are different kinds of taxes like income tax, transportation tax, entertainment tax, value added tax, etc.

Income tax is levied on the income. In our country, a person or the institution pays a certain rate to the government on the amount earned above the fixed amount. Persons, minimum expenditure depends on the personal status like married or unmarried, the number of dependent family members etc. Income tax is levied to the earning above the minimum expenditures (called the allowances). The limit of allowances is fixed by the government. The rate is subject to change by the time.

- Taxable income = Total income - Tax-free allowances
- Income Tax = Rate of tax % (in %) * Taxable income

**Example:**

A teacher's monthly salary is Rs. 13500, and the annual allowances are Rs. 140000. If the income above this is taxable at the rate of 15%, how much salary does he receives per month after the deduction of the income tax?

Monthly salary = Rs.13500

Annual salary = 12 \(\times\) Rs. 13500

= Rs. 162000

Allowances = Rs. 140000

Taxable income = Rs. 162000 - Rs. 140000

= Rs. 22000

Annual income tax = 15% of Rs. 22000

= \(\frac{15}{100}\) \(\times\) Rs. 22000

= Rs. 3300

Monthly Income tax = Rs. \(\frac{3300}{12}\) = Rs. 275.

\(\therefore\) Monthly Salary Received = Rs. 13500 - Rs. 275

= Rs. 13225.

If a factory or a company or any other business organization makes a profit, they distribute a certain amount of profit to their staff to encourage at their work.This additional amount of profit is called the bonus.The bonus is expressed in percentage.The percentage is decided by the body o executive committee of an organization. Therefore, the bonus is provided by the annual general meeting (AGM) of an organization.

A shopkeeper marks price (MP) fixed before selling to earn more profit but he deducts a certain amount in mark price due to various reason. Discount is the deducted amount given to a customer by shopkeeper while purchasing goods.The price at which the good is sold after the deduction of a discount amount is called selling price (SP).

- Actual discount (D) = Marked price (MP) - Selling price (SP)
- Discount percentage = \(\frac{Actual\;discount}{Marked\;price}\)*100

Vat is a tax levied on the supply of goods and services. Vat rely on a country which is determined annually by state govern. In a case of Nepal, currently, 13% VAT is charged. VAT is determined by adding taxes for different purposes. And it is charged on the actual selling price.

- VAT amount = Rate of VAT × Selling price
- SP with VAT = SP + VAt amount
- VAT% = \(\frac{VAT\;amount}{SP}\)×100

- Tax is a financial charge or other levy imposed upon a taxpayer (an individual or legal entity) by a state or the functional equivalent of a state to fund various public expenditures.
- Bonus means an extra payment (bonus payment) received for doing one's job well.
- Commission = fixed percentage of selling price
- Price after commission = selling price - commission amount
- Commission % = \(\frac{commission}{selling \;price}\)×100
- Taxable income = Total income - Tax-free allowances
- Income Tax = Rate of tax % (in %) × Taxable income
- VAT amount = Rate of VAT * Selling price
- SP with VAT = Sp + VAt amount
- VAT% = \(\frac{VAT\;amount}{SP}\)×100

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

The allowances on the basis of a number of dependent family members for a person earning Rs. 165000 annually is Rs. 120500. If the rate of tax on the rest is 30% find the amount paid as income tax.

Tax free income = Rs.120 , 500

Annual income = Rs.165 , 000

Taxable income = Rs . 165 , 000 - Rs. 120 , 500 = Rs. 44 , 500

Rate of income tax = 30%

Actual income

A person working in a foreign agency pays 30% upto Rs. 146000 and 40% from Rs. 146001 to Rs. 172000 as income tax. Find the tax paid the person if his annual salary is Rs.189500 and the allowance are Rs. 34500.

Annual income = Rs. 1 , 89 , 500

tax free amount = Rs. 34 , 500

Taxable amount = Rs. 1 ,89 500 - Rs. 34 , 500 = Rs. 1 , 55 , 000

Here , 30% income tax should be paid up to Rs. 1 , 46 , 000

Initial income tax = Rs . 1 , 46 , 000 \(\times\) \(\frac{30}{100}\) = Rs. 43 , 800

Taxable Income on which 40% tax is levied = Rs. 1 , 55 , 000 - Rs. 1, 46 , 000

= Rs . 9000

Again , income tax of Rs. 9000 = RS. 9000 \(\times\) \(\frac{40}{100}\) = Rs. 3 , 600

Total income tax = Rs. 43 , 800 + Rs. 3 , 600 = Rs. 47 , 400 Ans.

Find the rate of income tax if person pays Rs.14280 on his income of Rs. 82000 and the allowances of Rs.31000.

Annual income = Rs. 82 , 000

Tax free amount = Rs. 31 ,000

Taxable amount = Rs. 82 , 000 - Rs. 31 , 000 = Rs. 51 , 000

Total income tax paid = Rs. 14 , 820

Rate of income tax = \(\frac{rs.14 , 820}{rs.51 , 000}\) \(\times\) 100 = 28%. Ans.

Find the tax to be paid by a person or a company using the table below :

Annual taxable Income | Tax Rate |

1 - 10000 | 2.5% |

10 , 000 - 30 , 0000 | 4% |

30 , 000 - 1 , 00 , 000 | 5.25% |

1 , 00 , 000 - 10 lakhs | 12.75% |

(i) Annual income = Rs. 55000 , allowances = Rs . 47 , 000

(ii) Annual income = Rs. 1 , 75 , 000 , allowances = Rs. 65 , 000

(iii) , Annual income = Rs. 9 , 40 , 800 , allowances = Rs. 5 , 50 , 000

Annual income = Rs. 55000

Tax free income = Rs, 47 , 000

TAxable income = Rs . 55000 - Rs . 47 , 000 = Rs. 8000

From table table 2.5% tax is paid up to 1 - 10000

Hence , income tax of Rs. 8000 = Rs . 8000 \(\times\) \(\frac{2.5}{100}\) = Rs. 200

(ii). Annual income = Rs. 1 ,75 ,000

Taxfree income = Rs. 65 , 000

Taxable income = Rs. (1 , 75 000 - 65 , 000) = Rs . 1 , 10 , 000

Now , total income tax

= Rs. 10000 \(\times\) \(\frac{2.5}{100}\) + Rs. \(\times\) Rs. 20 , 000 \(\times\) \(\frac{4}{100}\) + Rs. 70 , 000 \(\times\) \(\frac{5.25}{100}\ + Rs. 10000 \(\frac{12.75}{100}\)

= Rs. 250 + Rs. 800 + 3 , 675 + Rs. 1 , 275 = Rs . 6000

(iii) Total income = Rs. 9 ,40 , 800

Tax free income = Rs. 5 , 50 ,000

Taxable income = Rs. 9 , 40 , 800 - Rs. 5, 50 , 000 = Rs. 3 , 90 , 8000

As in the above (ii) 2.5% is levied on Rs. 10 , 000 , 4% tax is levied on next Rs.20 , 000 and 5.25% is levied on the next Rs. 70 , 000

Now , remaining amount on taxable income of Rs. 3, 90 , 800 - (Rs. 10 , 000 + Rs. 20 , 000 + Rs. 70 , 000) = Rs. 2 , 90 , 800 , 12.75% tax is levied.

Now ,total income tax

= 250 + 800 + 3 , 675 + 37 , 077 = Rs. 41 , 802 Ans.

By selling a plot of land Rs. 2700000 an agent receives a comission of \(\frac{1}{2}\)% on the first 10 lakhs \(\frac{1}{4}\)% on the rest , how much amount will the landowner receive ?

Selling price of land = Rs. 2 ,70 , 000

Comission received on the sale of Rs. 10 ,00 ,000 at the rate of \(\frac{1}{2}\)%

= Rs. 10 , 00 , 000 \(\\times\) \(\frac{1}{2 \times 100}\) = Rs. 5000.

Again , rest amount = (27 , 00 , 000) - 10 , 00 , 000) = Rs. 17 , 00 , 000

Now , comission received on the sale of Rs. 17 , 00 , 000 at the rate of \(\frac{1}{4}\)%

= Rs. 17 , 00 , 000 \(\times\) \(\frac{1}{4 \times 100}\) = Rs. 4250.

Here , total comission recived by the agent = Rs. 5 , 000 + Rs. 4250

= Rs. 9250

Total amount received by landowner = Rs. 27 , 00 , 000 - RS. 9250

= Rs. 26 , 90 , 750 Ans.

A finacial company distributes 25% of the profit as bonus to its employee and each received Rs. 8000 as bonus . If the number of employee in that company were 60 , what was tht total profit of the company ?

Distributed profit as bonus for 60 workers = 60 \(\times\) Rs. 8000 = Rs. 480000

Let te profit of the company = x

By question ,

x \(\times\) \(\frac{25}{100}\) = Rs. 480000

\(\therefore\) x = \(\frac{Rs.480000 \times100}{25}\) = Rs. 1,92,000 Ans.

Because of the increase in the number of tourists a hotel made a profit of Rs. 2500000. If certain percentage of the was distributed among 75 workers of the hotel as bonus at the rate of Rs. 15000 per wokers , at what rate was the bonus distributed ?

ljTotal profit of hotel = Rs. 2500000

Total amount which is distributed for 75 workers = 75 \(\times\) Rs. 15000

= Rs. 11 , 25 , 000

\(\therefore\) Distributed bonus (%) = \(\frac{11,25,000}{25,00,000}\) \(\times\) 100% = 45%. Ans.

A commercial bank distributed one third of it's employee as the bonus . If the bank has distributed rs. 12000 to each of 140 employees, what was the total profit made by the bank ?

Total profit of bank = Rs. x (suppose)

Total amount which is distributed for 140 employees = 140 \(\times\) Rs. 12000

= Rs. 1 , 68 , 0000

By question ,

\(\frac{1}{3}\) \(\times\) x = Rs. 1 , 68 , 000

or , x= Rs. 168000 \(\times\) 3 = Rs. 5 , 04 , 0000 Ans.

What is the actual price of the first class ticket of a cultual program if it costs Rs. 98 including ^{}the entertainment tax 22.25% ?

Cost of ticket with entertainment tax = Rs.98

Let actual cost of Ticket= Rs. x

Now , Entertainment tax = 22.5% of x = x \(\times) \(\frac{22.5}{100}\) = 0.225

Here, x + 0.225x = Rs.98

or , x (1+0.225) = Rs.98

or. x(1.225) = Rs.98

\(\therefore\) x = Rs. \(\frac{98}{122.5}\) = Rs. 80

Hence , actual cost of ticket = Rs.80 Ans.

If in a restaurant' bill 10% service charge and 4% government tax is added, the statement of the bill is as below:

momo per plate | Rs.40 |

meatball one plate | Rs.75 |

Coke two bottles | Rs.35 |

Chicken Chilly one plate | Rs.80 |

Total | Rs.230 |

Find :

(i). the total service charge.

(ii). the government tax.

(iii). the total payable amount

(iv). if a total of Rs. 260.25 was paid including the 10% service charge. what was the government tax in percentage. ?

Service charge = 10% of rS.230 = 230 \(\times\) \(\frac{10}{100}\) = Rs. 23 Ans.

(ii) . Total bill with service charge = 230 + 23 = Rs. 253.

\(\therefore\) Government tax = 4% of 253 \(\times\) \(\frac{4}{100}\) = Rs. 10.12 Ans.

(iii). Total oayable amount = Rs. 230 + Rs. 10.12 + Rs. 23

= Rs. 263.12 Ans.

(iv) . Bill with the service charge on which government tax should be levied = Rs. 253.

Total payable bill with 10% service charge and including government tax = Rs. 260.25

\(\therefore\) Amount of goverrnment TAx = Rs. 260.25 - Rs. 253 = Rs.7.25

Here , government tax (%) = \(\frac{Amount. of gov. tax}{govt. taxable bill}\) \(\times\) 100

= \(\frac{7.25}{253}\) \(\times\) 100

= 2.865%

= 2.87% (approx) Ans.

© 2019-20 Kullabs. All Rights Reserved.