Commercial Arithmetic - Mathematics Form 1 Notes

• Introduction
• Currency Exchange Rates
• Profit and Loss
• Commission
• Past KCSE Questions on the Topic

Introduction

• In commercial arithmetic we deal with calculations involving business transaction.
• The medium of any business transactions is usually called the currency.
• The Kenya currency consist of a basic unit called a shilling.
• 100 cents are equivalent to one Kenyan shillings, while a Kenyan pound is equivalent to twenty Kenya shillings.

Currency Exchange Rates

• The Kenyan currency cannot be used for business transactions in other countries. To facilitate international trade, many currencies have been given different values relative to another. These are known as exchange rates.
• The table below shows the exchange rates of major international currencies at the close of business on a certain day in the year 201 5.The buying and selling column represents the rates at which banks buy and sell these currencies.
  

Note

• The rates are not always fixed and they keep on charging. When changing the Kenyan currency to foreign currency, the bank sells to you. Therefore, we use the selling column rate. Conversely when changing foreign currency to Kenyan Currency, the bank buys from you, so we use the buying column rate.
  

  Currency	Buying	Selling
  DOLLAR	102.1 472	102.3324
  STG POUND	154.0278	154.361 7
  EURO	109.6072	109.8522
  SA RAND	7.3332	7.3486
  KES/USHS	33.0785	33.2363
  KES/TSHS	20.91 23	21 .0481
  KES / RWF	7.231 3	7.3423
  AE DIRHAM	27.8073	27.8653
  CAN $	77.601 8	77.7661
  JAPNESE YEN	84.0234	84.1 964
  SAUDI RIYAL	27.2284	27.2959
  CHINESE YUAN	16.0778	16.1082
  AUSTRALIAN $	71.8606	72.0420

Example

Convert each of the following currencies to its stated equivalent

1. Us $305 to Ksh
2. 530 Dirham to euro

Solution

1. The bank buys Us 1 at Ksh 102.1472
   Therefore US $ 305 = Ksh (102.1472 x 305)
   = Ksh 31, 154.896
   = Ksh 31,1 54.00 (To the nearest shillings)
   The bank buys 1 Dirham at Ksh 27.8073
   Therefore 530 Dirham = Ksh (21.8073 x 530)
   = Ksh 11, 557.00 (To the nearest shillings)
   The bank sells 1 Euro at 1 09.8522
   Therefore 530 Dirham = 11, 557/109.8522
   = 105.170 Euros

Example

During a certain month, the exchange rates in a bank were as follows;

A tourist left Kenya to the United States with Ksh.1 000,000.On the airport he exchanged all the money to dollars and spent 1 90 dollars on air ticket. While in US he spent 4500 dollars for upkeep and proceeded to Europe. While in Europe he spent a total of 2000 Euros. How many Euros did he remain with? (3marks)

Solution

1000000 = 10893.25
   91.8
10893.25 − (190+4500) = 6203.25
6203.25 × 91.65 = 568, 278.86
568, 527 = 5470.30
 103.93
5470.30 − 2000 = 3470.30

Profit and Loss

• The difference between the cost price and the selling price is either profit or loss. If the selling price is greater than the cost price, the difference is a profit and if the selling price is less than the total cost price, the difference is a loss.
  
  Note
  
  Selling price − cost price = profit
  Percentage profit =    Profit    x 100
                               Cost price
  Cost price − selling price = loss
  Percentage loss =   Profit    x 100
                           Cost price

Example

Ollie bought a cow at sh 1 8000 and sold it at sh 21 000.What percentage profit did he make?

Solution

Selling price = sh 21 000
Cost price = sh 1 8000
Profit = sh (21, 000 − 18, 000)
= sh 3000
Percentage profit = 3000 x 100
                            18000
= 16²/₃%

Example

Johnny bought a dress at 3500 and later sold it at sh. 2800.what percentage loss did he incurs?

Solution

Cost price = sh 3500
Selling price = sh 2800
Loss = sh (3500 − 2800)
= Sh 700
Percentage loss = 700 x 100 = 20%
                          3500
Discount

A shopkeeper may decide to sell an article at reduced price. The difference between the marked price and the reduced price is referred to as the discount. The discount is usually expressed as a percentage of the actual price.

Example

The price of an article is marked at sh 1 20.A discount is allowed and the article sold at sh 96.Calculate the percentage discount.

Solution

Actual price = sh 120.00
Reduced price = sh 96.00
Discount = sh (120.00 – 96.00)
=sh 24
Percentage discount = ²⁴/₁₂₀ x 100
= sh 20%

Commission

A commission is an agreed rate of payment, usually expressed as a percentage, to an agent for his services.

Example

Mr. Neasa, a salesman in a soap industry, sold 250 pieces of toilet soap at sh 45.00 and 21 5 packets of determining at sh 75.00 per packet. If he got a 5% commission on the sales, how much money did he get as commission?

Solution

Sales for the toilet soap was 250 x 45 = sh 1 1 250
Sales for the detergent was 215 x 75 = sh 1 61 25
Commission = ⁵/₁₀₀( 11250+16125)
⁵/₁₀₀ x 27375 = sh1368

Example

A salesman earns a basic salary of sh. 9,000 per month. In addition he is also paid a commission of 5% for sales above sh. 15,000. In a certain month he sold goods worth sh. 1 20,000 at a discount of 2½%. Calculate his total earnings that month. (3 marks)

Solution

sales sh.120,000
net after discount ^97.5/₁₀₀ ×120,000 = 17,000
sales above sh.15,000 = 117,000 − 15,000
= kshs.102,000
commisiion ⁵/₁₀₀ ×102,000 = 5,100
total earnings = 9,000 + 5,100
= kshs 14,100

Past KCSE Questions on the Topic

1. The cash prize of a television set is Kshs 25000. A customer paid a deposit of Kshs 3750. He repaid the amount owing in 24 equal monthly installments. If he was charged simple interest at the rate of 40% p.a how much was each installment?
2. Mr Ngeny borrowed Kshs 560,000 from a bank to buy a piece of land. He was required to repay the loan with simple interest for a period of 48 months. The repayment amounted to Kshs 21,000 per month.
   Calculate
   1. The interest paid to the bank
   2. The rate per annum of the simple interest
3. A car dealer charges 5% commission for selling a car. He received a commission of Kshs 17,500 for selling car. How much money did the owner receive from the sale of his car?
4. A company saleslady sold goods worth Kshs 240,000 from this sale she earned a commission of Kshs 4,000
   1. Calculate the rate of commission
   2. If she sold good whose total marked price was Kshs 360,000 and allowed a discount of 2% calculate the amount of commission she received.
5. A business woman bought two bags of maize at the same price per bag. She discovered that one bag was of high quality and the other of low quality. On the high quality bag she made a profit by selling at Kshs 1 ,040, whereas on the low quality bag she made a loss by selling at Kshs 880. If the profit was three times the loss, calculate the buying price per bag.
6. A salesman gets a commission of 2.4 % on sales up to Kshs 100,000. He gets an additional commission of 1.5% on sales above this. Calculate the commission he gets on sales worth Kshs 280,000.
7. Three people Koris, Wangare and Hassan contributed money to start a business. Korir contributed a quarter of the total amount and Wangare two fifths of the remainder. Hassan’s contribution was one and a half times that of Koris. They borrowed the rest of the money from the bank which was Kshs 60,000 less than Hassan’s contribution. Find the total amount required to start the business.
8. A Kenyan tourist left Germany for Kenya through Switzerland. While in Switzerland he bought a watch worth 52 deutsche Marks. Find the value of the watch in:
   Swiss Francs.
   Kenya Shillings
   Use the exchange rtes below:
   1 Swiss Franc = 1 .28 Deutsche Marks.
   1 Swiss Franc = 45.21 Kenya Shillings
9. A salesman earns a basic salary of Kshs. 9000 per month. In addition he is also paid a commission of 5% for sales above Kshs 1 5000. In a certain month he sold goods worth Kshs. 1 20, 000 at a discount of 2½ %. Calculate his total earnings that month
10. In this question, mathematical table should not be used
    A Kenyan bank buys and sells foreign currencies as shown below
    

    	Buying (In Kenya shillings)	Selling (In Kenya shillings)
    1 Hong Kong dollar	9.74	9.77
    1 South African rand	12.03	12.11

    A tourists arrived in Kenya with 105 000 Hong Kong dollars and changed the whole amount to Kenyan shillings. While in Kenya, she pent Kshs 403 897 and changed the balance to South African rand before leaving for South Africa. Calculate the amount, in South African rand that she received.
11. A Kenyan businessman bought goods from Japan worth 2,950 000 Japanese yen. On arrival in Kenya custom duty of 20% was charged on the value of the goods.
    If the exchange rates were as follows
    1 US dollar = 1 1 8 Japanese Yen
    1 US dollar = 76 Kenya shillings
    Calculate the duty paid in Kenya shillings
12. Two businessmen jointly bought a minibus which could ferry 25 paying passengers when full. The fare between two towns A and B was Kshs. 80 per passenger for one way. The minibus made three round trips between the two towns daily. The cost of fuel was Kshs 1 500 per day. The driver and the conductor were paid daily allowances of Kshs 200 and Kshs 150 respectively. A further Kshs 4000 per day was set aside for maintenance.
    1. One day the minibus was full on every trip.
       
       1. How much money was collected from the passengers that day?
          
       2. How much was the net profit?
    2. On another day, the minibus was 80% on the average for the three round trips. How much did each business get if the days profit was shared in the ratio 2:3?
13. A traveler had sterling pounds 91 8 with which he bought Kenya shillings at the rate of Kshs 84 per sterling pound. He did not spend the money as intended. Later, he used the Kenyan shillings to buy sterling pound at the rate of Kshs. 85 per sterling pound. Calculate the amount of money in sterling pounds lost in the whole transaction.
14. A commercial bank buys and sells Japanese Yen in Kenya shillings at the rates shown below
    

    Buying	0.5024
    Selling	0.5446

    A Japanese tourist at the end of his tour of Kenya was left with Kshs. 30000 which he converted to Japanese Yen through the commercial bank. How many Japanese Yen did he get?
15. In the month of January, an insurance salesman earned Kshs. 6750 which was commission of 4.5% of the premiums paid to the company.
    1. Calculate the premium paid to the company.
    2. In February the rate of commission was reduced by 662/3% and the premiums reduced by 1 0% calculate the amount earned by the salesman in the month of February
16. Akinyi, Bundi, Cura and Diba invested some money in a business in the ratio of 7:9:1 0:1 4 respectively. The business realized a profit of Kshs 46800. They shared 1 2% of the profit equally and the remainder in the ratio of their contributions. Calculate the total amount of money received by Diba.
17. A telephone bill includes Kshs 4320 for a local calls Kshs 3260 for trank calls and rental charge Kshs 2080. A value added tax (V.A.T) is then charged at 15%, Find the total bill.
18. During a certain period. The exchange rates were as follows
    1 sterling pound = Kshs 1 02.0
    1 sterling pound = 1 .7 us dollar
    1 U.S dollar = Kshs 60.6
    A school management intended to import textbooks worth Kshs 500,000 from UK. It changed the money to sterling pounds. Later the management found out that the books the sterling pounds to dollars. Unfortunately a financial crisis arose and the money had to be converted to Kenya shillings. 
    Calculate the total amount of money the management ended up with.
19. A fruiterer bought 1 44 pineapples at Kshs 1 00 for every six pineapples. She sold some of them at Kshs 72 for every three and the rest at Kshs 60 for every two. If she made a 65% profit, calculate the number of pineapples sold at Kshs 72 for every three.