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# Business Mathematics Assignment Questions Answers

Subject: Business Mathematics Assignment

Q1

**1.(a)** Rahma told Sumaya that if the Means and the Extremes of a proportion are interchanged the resulting ratio forms a proportion. Do you agree with Rahma? Explain Why and why not stating and proving with an example. **[5 Marks]**

**1.(b)** Sumaya thought that if the same number is added to each term of a proportion, the resulting ratio form a proportion. Do you agree with Sumaya? Illustrate by stating and proving with an example. **[5 Marks]**

Q2

**(1). **Mr. Majid is a wholesaler in Mutrah market. The main items he sell in the Seeb market are Wheat, Rice and Sugar. Jasim LLC is a retailer in Barka who buys wheat, rice and sugar from Majid, in whole sale since ten years for the retail shop. As they are in a very good trade relationship Majid planned to give him a trade discount of 20%, 25% and 30% on wheat, rice and sugar respectively. If Jasim LLC, gets such a discount from Majid , they will be able to sell the items in the below mentioned list prices:

Items | Total list price |

Wheat ( 500 kg) | OMR 899.50 |

Rice ( 1000 kg ) | OMR 1002.90 |

Sugar ( 900 kg) | OMR 999.50 |

**You are required to:**

(a) What price Jasim LLC should pay to buy the Wheat to Mr. Majd, the wholesaler? **(1 Mark)**

(b) What price Jasim LLC should pay to buy the Rice to Mr. Majid, the wholesaler? **(1 Mark)**

(c) What price Jasim LLC should pay to buy the Sugar to Mr. Majid, the wholesaler? **(1 Mark)**

**(2).** As the summer approaches Mr. Busaidi is in search of good quality refrigerator to be replaced in his house. With an intention to buy a refrigerator he went to Lulu hypermarket. There he found three different companies refrigerator at different prices. They were as follows :

Item | Net Price | Trade Discount Amount |

Toshiba refrigerator | OMR 259.99 | OMR 18 |

Geepas refrigerator | OMR 189.99 | OMR 25 |

Whirpool refrigerator | OMR 226.50 | OMR 20 |

By seeing the prices and discount amount Mr.Busaidi was confused to buy which refrigerator. You are required to help him in choosing the best refrigerator in terms of less price.

(a) Determine the discount rate applied for Toshiba refrigerator**. (1 Mark)**

(b) Determine the discount rate applied for Geepas refrigerator. **(1 Mark)**

(c) Determine the discount rate applied for Whirpool refrigerator. **(1 Mark)**

(d) Which refrigerator you will suggest Mr.Busaidi to buy in terms of discount rate. **(1 Mark)**

**(3).** Omani mark LLC exports dates to various countries in the brand name Omani Khajoor. Two main importers and trade partners of Gulf mark LLC are India and Srilanka. Omani mark LLC sold 6000 kilograms and 9000 kilograms of Omani Khajoor to India and Srilanka respectively.

**(a)** The invoice date with India was July 06,2019, and the goods were sold for OMR 24000. The terms of the payment was 6/10,n/30.The invoice was paid on July 12,2019.

**You are required to :**

(i) Find out whether India is eligible for a discount. **(0.5 Mark)**

(ii) If yes, find the amount of discount. **(0.5 Mark)**

(iii) Find also, the total amount paid by India. **(0.5 Mark)**

**(b)** The invoice date with Srilanka was July 10, 2019, and the goods were sold for OMR 36000. The terms of the payment was 4/10 E.M.O is received. The invoice was paid on August 5, 2019.

**You are required to :**

(i). Find out whether Srilanka is eligible for a discount. **(0.5 Mark)**

(ii). If yes, find the amount of discount. **(0.5 Mark)**

(iii). Find also, the total amount paid by Srilanka. **(0.5 Mark)**

Q3

Fatima Super market [retailer] buys an article from ABC Hypermart [wholesaler] at OMR 5000 and the wholesaler charges a sales tax at the rate prescribed rate of 8%. The retailer fixes the price at OMR 7000 and charges sales tax at the same rate to Mr. Rahim [customer].

**Apply VAT system of sales tax calculation to answer the following.**

(i). What is the price that a consumer [Mr. Rahim] has to pay to buy the article? **[1 Mark]**

(ii). What is the VAT that a consumer [Mr. Rahim] has to pay to buy the article? **[1 Mark]**

(iii). Find the input tax and output tax for the retailer [Fatima Super market]. **[1 Mark]**

(iv). Find the input tax and output tax for the wholesaler [ABC Hypermarket].**[1 Mark]**

(v). How much VAT does the retailer pay to the government? **[1 Mark]**

(vi). How much VAT does the wholesaler pay to the government? **[1 Mark]**

(vii). How much VAT the government received in total? **[ 1 Mark]**

**(2).** ** “Amount paid by the customer [Rahim] at the final stage of supply chain is equal to amount received by government in stages”**. Do you agree with the statement? Justify your answer in your own words with correct example

**[3 Marks]**

Q4 :

Mr. Salim, Mr, Ahmed, Mr. Khalid and Mr. Sulaiman are employee of HygeineX Farma LLC. During the COVID-19 lockdown period they prepared total of 36000 pieces of hand sanitizer bottles. The ratio of preparation among the four are as 10:25: 35: 20. The company pays them on piece rate basis, 50 baisa per piece. Calculate their gross pay in terms of OMR. **(4 Marks)**

**(2). **Mr. Bassam is a sales executive for Medicare LLC. During the COVID-19 lockdown period he made OMR 275000, retail distribution contracts.

Calculate the gross pay of Mr. Bassam if

(i). He get a straight commission of 1.5% with an advance of OMR 500. **(1.5 Marks)**

(ii). He is paid commission as

1% on OMR 1 to OMR 150000

2% on OMR 150001 to OMR 200000,

2.5% on OMR 200001 to OMR 250000

and 3% on all remaining sales. **(2.5 Marks)**

(iii) He get a OMR 1000 monthly salary plus 2.35% commission over OMR 225000. **(2 Marks)**

Q5 :

Muscat chocolates Company purchases equipment on January 1, 2017, at a cost of OMR 100000. The asset is expected to have a service life of 4 years and a residual value of OMR 20000.

**Instructions:**

(a) Calculate the annual rate of depreciation. Amount of depreciation for each from 2017 to 2019 using the straight-line depreciation method. **[4 Marks]**

(b) Calculate the amount of depreciation for each from 2017 to 2019 using the reducing balance method. **[3 Marks]**

(c) What would be the difference in the depreciation expense for the year ending 31st December 2019 based on using either the straight-line method or the reducing-balance method? **[1 Mark]**

(d) On what basis should management select from these two methods to depreciate the machine? Justify in your own words **[1 Mark]**

(e) What do you feel may be the difference between these two methods of computing depreciation? Explain in your own words **[1 Mark]**

## Answer

**Answer 1:**

(a). Yes, if the Means and Extremes of a proportion are interchanged the resulting ratio forms a proportion. When the ratios are in proportion the product of means is equal to the product of the extremes. If the means and extremes are interchanged their product will still remain the same and hence the resulting ratios will be in proportion.

Eg. Ratio in proportion = 10 : 20 :: 5 : 10

10/20 = 5/10 = ½

Means 20 and 5

Extremes are 10 and 10

Product of means = product of extremes

20x 5 = 10x10

If they are exchanged:

Means = 10 and 10

Extremes are 20 and 5

Ratio = 20: 10 :: 10: 5

20/10 = 10/5 = 2/1

(b) No, if the same number is added to each term of a proportion, the resulting ratio will not form a proportion.

Eg: Ratio in proportion = 10 : 20 :: 5 : 10

10/20 = 5/10 = ½

Add 2 to each term, new terms are : 10+2 , 20+2, 5+2, 10+2

= 12, 22, 7, 12

The terms are not in proportion as 12/22 is not equal to 7/12.

**Answer 2:**

(1).

(a) Wheat (500 kg), Total List Price = OMR 899.50

Trade discount 20% on wheat

Discount= 899.50*20/100 = 179.90

Net Price = List Price – Trade discount

=899.50 – 179.90 = OMR 719.60

Jasim LLC should pay OMR 719.60 for the Wheat (500 kg) to Mr. Majd, the wholesaler.

(b) Rice (1000 kg), Total List Price = OMR 1002.90

Trade discount 25% on rice

Discount= 1002.90*25/100 = 250.725

Net Price = List Price – Trade discount

=1002.90 – 250.725 = OMR 752.175

Jasim LLC should pay OMR 752.175 for the Rice (1000 kg) to Mr. Majd, the wholesaler.

(c) Sugar (900 kg), Total List Price = OMR 999.50

Trade discount 30% on wheat

Discount= 999.50*30/100 = 299.85

Net Price = List Price – Trade discount

=999.50 – 299.85 = OMR 699.65

Jasim LLC should pay OMR 699.65 for the Sugar (900 kg) to Mr. Majd, the wholesaler.

(2)

(a) Net price for Toshiba refrigerator = OMR 259.99

Trade Discount= OMR 18

List price = Net price +Trade Discount = 259.99+18 = OMR 277.99

Discount Rate = Discount/list price x 100

= 18/277.99 x 100 = 6.475%

(b) Net price for Geepas refrigerator = OMR 189.99

Trade Discount= OMR 25

List price = Net price +Trade Discount = 189.99+25 = OMR 214.99

Discount Rate = Discount/list price x 100

= 25/214.99 x 100 = 11.628%

**(c) **Net price for Whirpool refrigerator = OMR 226.50

Trade Discount= OMR 20

List price = Net price +Trade Discount = 226.5 + 20 = OMR 246.50

Discount Rate = Discount/list price x 100

= 20/246.50 x 100 = 8.114%

(d) The discount rates are as follows:

Item | Discount Rate |

Toshiba refrigerator | 6.475% |

Geepas refrigerator | 11.628% |

Whirpool refrigerator | 8.114% |

Since the trade discount is maximum in Geepas refrigerator (11.628%). Thus in terms of discount arte Geeaps Refrigerator is suggested to Mr. Busaidi.

**(3)**

- Sale of Omani Kajoor to India:

Quantity = 6000 kg

Invoice date = July 06, 2019

Selling price = OMR 24,000

Terms of Payment = 6/10,n/30

Invoice was paid on = July12, 2019

2. The payment terms offers discount of 6% if the payment is made within 10 days of invoice. Since the payment is made within 10 days from the invoice date , the discount rate will be available to India at 6%

3. The amount of discount = 24,000*6/100 = OMR 1440

The amount of discount to India is OMR 1,440

4. The total amount paid by India = selling price – discount

= 24000 – 1440 = OMR 22,560

(b) Sale of Omani Kajoor to Srilanka:

Quantity = 9000 kg

Invoice date = July 10, 2019

Selling price = OMR 36,000

Terms of Payment = 4/10 EMO

Invoice was paid on = August 5, 2019

(i) The payment terms offers discount of 4% if the payment is made within 10 days from the end of the month . Since the payment is made within 10 days from the end of the month , the discount rate will be available to Srilanka at 4%.

- The amount of discount= 36000x 4/100 = 1,440 The amount of discount to Srilanka is OMR 1,440
- The total amount paid by Srilanka = selling price – discount

= 36000 – 1440 = OMR 34,560

**Answer 3:**

(i) Mr. Rahim has to pay The price + Sales Tax @ 8%

Price of the article = 7000

Tax @ 8% = 560

Total amount paid by the customer = OMR 7560

Mr. Rhaim Has to pay OMR 7560 to buy the article

(ii) The VAT that a consumer has to pay to buy the article is OMR 560

(ii) Input and output tax for the retailer:

Input tax = Tax paid by the retailer to the wholesaler

Price paid by the retailer = OMR 5000

Tax @8% = OMR 400

Total amount paid by the retailer = OMR 5400

Output tax = tax realized by the retailer from the customer

Tax realized by the retailer from the customer = OMR 560

VAT paid by the retailer = 560- 400 = OMR 160

(iv) Input and output tax for the wholesaler:

Input tax = NIL

Output tax = tax realized by the wholesaler from the retailer

Tax realized by the wholesaler from the retailer = OMR 400

VAT paid by the retailer to the government:

Vat paid = output tax of retailer – input tax of retailer

= OMR 560- OMR 400 = OMR 160

(v) VAT paid by the retailer to the government = OMR 160

VAT paid by the wholesaler to the government:

Vat paid = output tax of wholesaler – input tax of wholesaler

= OMR 400 - OMR 0 = OMR 400

(vi) VAT paid by the wholesaler to the government = OMR 400

(vii) Total VAT received by the government = VAT paid by wholesaler + VAT paid by the retailer

= OMR 400 + OMR 160= OMR 560

(2) Yes, the amount paid by the customer Rahim at the final stage of supply chain is equal to the amount received by government received in stages.

The Sales tax paid by the customer Rahim = OMR 560

VAT received by Government from wholesaler = OMR 400

VAT received by Government from retailer = OMR 160

Total Tax (VAT) received by government in stages = 400 + 160 = OMR 560

It can be observed from above example that the amount of tax paid by the customer is equal to the tax received by government in stages.

VAT applies to goods at various stages in supply chain. In the end the tax is paid by the consumer. Everyone in the supply chain who is a buyer as well as the seller get the adjustment for input and output tax. However the customer is the end user and only has to pay tax. Thus the total tax received by the government in stages is equal to the tax paid by the consumer.

**Answer 4:**

**(1)**

Gross pay under piece rate basis = no of pieces produced x Rate per piece

Pieces of hand sanitizer bottles made by each employee and their gross pay:

Employee | Units produced | Rate per unit | Gross pay | Gross pay in OMR |

Mr. Salim | 36000x10/90 = 4000 | 50 Baisa | 200000 baisa | OMR 200 |

Mr.Ahmed | 36000x25/90 = 10000 | 50baisa | 500000 baisa | OMR 500 |

Mr. Khalid | 36000x35/90 = 14000 | 50 baisa | 700000 baisa | OMR 700 |

Mr. Sulaiman | 36000x20/90 = 8000 | 50baisa | 400000 baisa | OMR 400 |

(2)

Mr. Bassam made retail distribution contracts of OMR 275000

(i) Gross pay if straight commission of 1.5% with an advance of OMR 500:

Sales Commission = 275000x 1.5%= OMR 4125

Less Draw= __OMR 500__

Gross pay = OMR 3625

(ii) Mr. Bassam Gross pay:

Upto 150000 1% = 150000 x 1/100 = OMR 1500

From 150001 to 200000 2% = 50000 x2/100 = OMR 1000

From 200001 to 250000 2.5% = 50000 x2.5/100 = OMR 1250

Above 250000 3% = 25000x3/100 = OMR 750

Gross Pay = 1500+ 1000+ 1250 + 750 = OMR 4500

(iii) Mr. Bassam gets:

Salary monthly = OMR 1000

Commission 2.35% over OMR 225000 = 50000x 2.35/100 = OMR 1175

Gross pay = 1000+ 1175 = OMR 2157

**Answer 5:**

Muscat Chocolates Company purchases equipment:

Date of purchase = January 1 2017

Cost = OMR 100000

Expected service life = 4 years

Residual value = OMR 20000

(a) Annual rate of depreciation on straight –line depreciation on method

Annual depreciation = (100000 – 20000)/4 = 80000/4 = 20000

Annual Depreciation = OMR 20000 for each year from 2017 to 2019

(b) Amount of depreciation for each year from2017 to 2019 using reducing balance method:

Depreciation rate = 1 – (scrap value /cost )^(1/4)

= 1 – (20000/100000)^0.25 = 33.13%

Year | Book value at the beginning of the year | Depreciation at 33.13% | Written Down Value at the end of the year |

2017 | 100000 | 33130 | 66870 |

2018 | 66870 | 22154 | 44716 |

2019 | 44716 | 14814 | 29902 |

2020 | 29902 | 9906 | 19996 |

(c) The difference in the depreciation expense for the year ending 31st December 2019 based on using either the straight-line method or the reducing-balance method:

Depreciation under straight line method = OMR 20000 Depreciation under Written down value method = OMR 14814

The deprecation under Written down value (reducing –balance) method is more by OMR 5186

(d) The management should select from these two methods to depreciate the machine based upon the profitability of the firm. If the firm has high profits now which will decline later it can choose reducing balance method to reduce the taxable profit else straight line method.

(c) The written down value method seems more technical. In the starting years there is less repair and maintenance cost of machinery and hence more depreciation but as the machine is used it needs more repaid and maintenance. The depreciation in later years is reduced. Thus the total expenditure related with the machine or equipment is balanced out throughout the life of the asset.

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