Business Mathematics Assignment Questions Answers

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:

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)

1. 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%.

1. The amount of discount= 36000x 4/100 = 1,440  The amount of discount to Srilanka  is OMR 1,440
2. 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:

(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%

(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.