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Commercial arithmetic Questions

 

1.  Jane is a sales executive earning a salary of Ksh. 20,000 and a commission of 8% for the sales in excess of Ksh 100,000. If in January 2010 she earned a total of Ksh.48, 000 in salaries and commissions.

  1. Determine the amount of sales she made in that month   (4 mks)
  2. If the total sales in the month of February and March increased by 18% and then dropped by 25% respectively. Calculate

 (i) Jane’s commission in the month of February (3 mks)

 (ii) Her total earning in the month of March   (3 mks)

2.  Wekhomba bought a laptop in Uganda for Ush.1, 050,000. He then paid 60 US dollars as transportation charges to Kenya. On arrival in Kenya he paid duty and sales tax amounting to 55% of the cost in Uganda. He then gave it to a friend in Tanzania tax free. If the exchange rates were I US dollar = Ush 1016, 1Ksh = Ush 24.83 and Tsh 1 = Ksh 0.0714

(a) Calculate the total expenses in Kenya shillings incurred by Wekhomba    (3 mks)

(b) Find the expenditure on transportation and taxes as a percentage of the total

expenditure    (2 mks)

 (c) What is the total value of the laptop in Tanzanian shillings    (2 mks)

 (d) Find the overall increase in value of the laptop as percentage of the buying price  (3 mks)

3.  Wekesa deposited a certain amount of money in bank that paid compound interest at the rate of 20% P.A. Calculate to the nearest year the time he would have to wait for his investment to tripple.     (3 mks)

4.  A Kenya scholar to Japan exchanged converted Kenyan shillings to Yens. He received a total of 36,632.8 Yens. If the bank rates were as below, find how much to the nearest shilling he exchanged.

Buying selling

100 Japanese Yens Ksh 62.76 63.16  (2mks)

5.  Ann bought 24 trays of eggs at sh 225 each. Each tray contains 30 eggs. 54 eggs got broken  during transportation. At what price must he sell each egg in order to realize a profit of 22%.  Answer to the nearest 1 shilling. (4mks)

ecolebooks.com

6.  A man invests Ksh 10000 in an account which pays 16% interest p.a. The interest is compounded quarterly. Find the interest earned after 1 ½ years to the nearest shilling. (4mks)

7.  On Monday this currency exchange rate was

1 Euro (E) = Kshs.95.65

1 US dollar($) = Ksh.76.50

A gentle man Tourist decided to exchange half of his 2400E into Dollars.

Calculate to 2 decimal places the number of dollars he received. (3 marks)

8.  A trader sold an article at sh.4800 after allowing his customer a 12% discount on the marked price of the article. In so doing he made a profit of 45% .

  1. Calculate
    1. the marked price of the article. (3 marks)

 

  1. the price at which the trader had bought the article (2 marks)
  1. If the trader had sold the same article without giving a discount. Calculate the percentage profit he would

have made. (3 marks)

  1. To clear his stock, the trader decided to sell the remaining articles at a loss of 12.5% (Calculate the price at which he sold each article. (2 marks)

    9.  A Kenyan businessman bought a washing machine in Europe at 500 Euros. On coming back, the Kenyan government imposed a 120% import duty and a 50% sales tax. He decided to sell the washing machine at a profit of ksh. 32,800.

Calculate

(a) Import duty  (2 mks)

(b) Sales tax  (2 mks)

(c) Percentage profit (3 mks)

(d) Selling price  (3 mks)

 Take 1 Euro Є = 95 Kenya shillings

10.  A farmer made a loss of 28% by selling a goat for Sh.1440. What percentage profit would he have made if he had sold the goat for Sh.2100? (3mks)

11.  A drapper bought some shirts and some trousers from a wholesaler Y at Sh.200 per shirt and Sh.600 per trouser, spending a total of Sh.22, 000. If he had bought the same items from wholesaler X, he would have paid 25% more for a shirt and 15% less for a trouser and he would have spent Sh.700 more.

  1. Write a simultaneous equation to represent the above information.(1mk)
  2. Determine the number of each item he bought  (3mks)
  3. He sold all the items as a profit of 50% per shirt and 30% per trouser. Find the total profit he made if he bought from wholesaler X. (3mks)
  4. Calculate to the nearest whole number, the percentage profit he made if he bought from wholesale Y  (3mks)

 

12.  Chepkurui imports rice from the United States at an initial cost of 500US Dollars per tonne. He then pays 20% of this amount as shipping costs and 10% of the same amount as custom duty. When the rice reaches Mombasa he has to pay 5% of the initial cost to transport it to Nairobi.

(a)  Given that on the day of this transaction the exchange rate was 1US Dollar = Ksh 76.60, calculate the total cost of importing one tonne of rice up to Nairobi in Kenya Shillings

(4mks)

(b)  Chepkurui intends to make a profit of 20%. Giving your answer to the nearsest ten cents, calculate the price at which he must sell the rice per kilogram (4mks)

(c)  If on the day that he completes the sale of this import he changes the total collection back to US Dollars at the rate of 1US Dollar = Ksh 78.20, calculate the actual profit that Chepkurui realized correct to three decimal places (2mks)

 

13.  The purchase price of a TV consists of sh.4600 deposit and 8 equal monthly installments of sh.840. Given that the carrying charge is sh.2800. Find the cash price (3mks)

14.  Three business partners Asha, Ogola and Jane contributed ksh.60,000, ksh.85,000 and ksh.105,000 respectively. They agreed to put 25% of the profit back into the business each year. They also agreed to put aside 40% of the remaining profit to cater for taxes and insurance. The rest of the profit would then be shared among the partners in the ratio of their contributions. At the end of the first year the business realized a gross profit of ksh.225,000.

  1. Calculate the amount of money Jane received more than Asha at the end of the year (5mks)
  2. Ogola further invested ksh.25,000 into the business at the beginning of the second year. Given that the gross profit at the end of the second year increased in the ratio of 10:9 and that 40% of it was shared, calculate Ogola’s share of the profit at the end of the second year (5mks)

15.  A man imported a vehicle at Shs. 600,000 and sold it at Sh. 1,080,0000. Find his percentage profit if he spent sh. 60,000 for clearing the vehicle from the port and a further sh. 40,000 for shipping. ( 3 marks )

16.  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:-

 (a) Swiss Francs

 (b) Kenya shillings  (3 marks)

 Use the exchange rates below

 1 Swiss Franc = 1.28 Deutsche marks

 1 Swiss Franc = 45.21 Kenya shillings

 

17.  Juanita sold goods worth ksh 95,000 and earned a total commission of Ksh 4,500. If the commission on the first Ksh. 50,000 was half of the total commission, what were the two rates of commission? (4mks)

18.  Mr. Sitienei sold a house to Mr. Lagat at a profit of 10%. Mr. Lagat then sold it to Mr. Rotich at a profit of 5%. Mr. rotich paid Ksh 110,000 more than Mr. Lagat for the house. Find how much Mr. Rotich paid for the house. (3mks)

19.  A Kenya bank buys and sells foreign currencies as shown below.

 Buying (Ksh) Selling Ksh

1 Euro 84.15  84.26

100 Japanese yen  65.37  65.45

 A Japanese traveling from France in Kenya with 5000 Euros. He converted all the 5000 Euros to  Kenya shillings at the bank. While in Kenya, he spent a total of Ksh. 289850 and then converted  the remaining Kenya shillings to Japanese Yens at the bank. Calculate the amount in Japanese  Yen that he received.  (3mks)

20.  Kimani bought a car at kshs. 120,000. Its value depreciated by 8% per year for the first 2 years and by 12% per year for the subsequent years.

  1. Determine the value of the car after 6 years. (4 mks)

 

  1. After 6 years, the car was sold through an agent at 25% more than its value. If the sales price was to be taken as its value after depreciation, calculate the average monthly rate of depreciation for the six years. (6 mks)

21.  Muthoni went to a shop and bought 50 packets of milk and 25 packets of salt all for Kshs.200.00. She sold the milk at a profit of 28% and the salt at a profit of 24% thereby making a net profit of Kshs.53.50. Find the cost price of a packet of milk and a packet of salt. (4 mks)

22.  The cost of a camera outside Kenya is US$1000. James intends to buy one camera through an agent who deals in Japanese Yen. The agent charges him a commission of 5% on the price of the camera and further 1260 Yen as importation tax. How many Kshs. Will he need to send to the agent to obtain the camera, given that:- (3 mks)

1 US$ = 105.00 Yen.

1 US$ = Kshs.63.00

23.  When shop keeper sells articles at sh. 240.50 each he makes a profit of 25% on the cost price. During a sale he reduces the price of each article by sh. 22.90. Calculate the percentage profit on an article sold at the sale price.  (3 marks)

24.  Factorise the expression Image From EcoleBooks.com (2 marks)

25.  In certain day the bank rates for changing dollars to shillings are given below.

Buying sellingDollar 78.4379.25
An American tourist changed US dollar 1500 to shillings, but then had to return to U. S. A immediately and changed all the shillings back to dollars using the same rates. How much did he lose? ( 3 marks)
26.  Find the angle  in degrees from the figure below

27.  In the diagram below, determine the equation of the line XY in the form y = mx + c  

28.  Find the equation of a line which passes through the point (2, 3) and is perpendicular to
y – 3x+ 1 = 0, giving your answer in the form y = mx + c

29.  T is the mid-point of line XY where X is point (1,4) and Y is the point (-5, 10). Find the
 equation of a line, L2 which is perpendicular to line XY and goes through point T

30.  (a) On the grid provided below, plot points A(2,1) B(-4,3) and C(2,5)
b) Given that the gradient of CD = -1 and CD =AD locate D and complete the
quadrilateral ABCD
 (c) What name is given to quadrilateral ABCD?
31.  In the figure below (not drawn to scale), PQRS is a rectangle and P and Q are the points
(3, 2) and (1,4) respectively

 Given that the equation of the line PQ is y =3x -7, find:
The equation of line QR
 

  1. The coordinates of point R
  2. The coordinates of point S

 

32.  OABC is a trapezium such that the coordinates of O, A , B and C are (0, 0), (2, -1), (4, 3)

and (0, y)

(a) Find the value of y  

 (b) M is the mid-point of AB and N is the mid-point of OM. Find in column form

  (i) the vector AN  

  (ii) the vector  NC

  (iii) Vector AC  

(c) Hence show that A, N and C are collinear  

 

33.  Use ruler and a pair of compasses only in this question.

 (a) Construct triangle ABC in which AB = 7 cm, BC = 8 cm and ∠ABC = 600.

 (b) Measure (i) side AC (ii) ∠ ACB

 (c) Construct a circle passing through the three points A, B and C. Measure the radius of the

circle.

(d) Construct ∆ PBC such that P is on the same side of BC as point A and ∠ PCB = ½ ∠ ACB,


∠ BPC = ∠ BAC measure ∠ PBC.

 

34.  ABCD is a parallelogram with vertices A (1,1) and C(8,10). AB has the equation

4x -5y = -1 and BC has the equation 5x – 2y = 20. Determine by calculation;

 (a) the co-ordinates of the point M where the diagonals meet  

 (b) The co-ordinates of the vertices B and D  

 (c) the length of AB correct to 4 significant figures

 

35.  The table shows corresponding values of x and y for a certain curve;

x

1.0

1.2

1.4

1.6

1.8

2.0

2.3

y

6.5

6.2

5.2

4.3

4.0

2.6

2.4

 

 

 

 

Using 3 strips and mid-ordinate rule estimate the area between the curve, x-axis,

  the lines x =1 and x =2.2

 

 

Commercial arithmetic Answers

1

  1. 48, 000 – 20, 000

= 28, 000

Image From EcoleBooks.com

= Ksh. 350, 000

Sales 350, 000 + 100, 000 = 450, 000

  1. (i) Sales in February

Image From EcoleBooks.com

Image From EcoleBooks.com

(ii) Image From EcoleBooks.com

Commission Image From EcoleBooks.com

Image From EcoleBooks.com

M1

 

M1

 

 

 

 

M1

A1

 

M1

 

M1

A1

 

 

M1

 

 

M1

 

A1

 

 

 

 

 

 

 

exp

2

Total expense

(a) Image From EcoleBooks.com

Image From EcoleBooks.com

In Ksh. Image From EcoleBooks.com

(b) Image From EcoleBooks.com

= 37.81%

 

(c) Image From EcoleBooks.com

 

(d) Image From EcoleBooks.com

Image From EcoleBooks.com

 

M1

 

 

 

M1

A1

 

M1

A1

 

M1

A1

 

 

M1

M1

A1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

exp

attempt to simplify

3

A = 3P

Image From EcoleBooks.com

3 = (1.2)n

Image From EcoleBooks.com

Image From EcoleBooks.com

 

M1

 

 

 

 

M1

 

A1

 
  

3

 

4.

100 Yens = 63.16 (Bank sold Yen)

36632.8 Yen = Image From EcoleBooks.com

= 23137.27648

= ksh 23137.

 

 

M1

 

A1

 
  

02

 

5.

No of good eggs = 24 x 30 – 54

 = 666

Total cost = 24 x 225

 = shs 5400

Cost with profit of 22% expected =

 Image From EcoleBooks.com

 = 6588

New price per egg = Image From EcoleBooks.com

 = 9.892

 = sh 10.00

M1

 

 

 

 

 

M1

 

 

M1

 

A1

 

 

 

 

 

 

 

  

04

 

6.

Image From EcoleBooks.com

 

 

 

M1

 

 

 

A1

 

 

M1

A1

 

  

04

 

7

½ of 2400E = 1200E

In ksh. = 1200E x 95.65

= Ksh.114,780

Number of dollar = Kshs.114,780

76.50

= sh1500.39

 

M1

 

M1

 

A1

 
  

3

 

8

SECTION B (50 MARKS)

 

Selling price = 88/100 of marked price

(a)

  1. 4800 = 88/100 of m.p

4800/88 x 100 = m.p

  = sh.5454.54

 

  1. 145/100 of buying price = 4800

    buying price = 48000 x 100

    145

    = 3310.34

     

     

(b) 5454.54 – 3310.34 x 100

3310.34

 

 = 0.6477 x 100

= 64.77%

 

 

 

 

  1. 87.5 of 3310.34

    100

 

= 2,896.55

10

Image From EcoleBooks.com

Image From EcoleBooks.com

 

5%

M1

 

M1

 

A1

3

 

11

200s + 600t = 22 000

250s + 510t = 22 700

 

1000s + 3000t = 110 000

1000s + 2040t = 90800

960t = 19 200

t = 20

s = 40

(0.5 × 200 × 20) + (0.3 × 510 × 40)

 

2500 + 6120 = 8620

Image From EcoleBooks.com+ Image From EcoleBooks.com

2000Image From EcoleBooks.com7200

Image From EcoleBooks.com%

19%Image From EcoleBooks.com

B1

 

 

M1

 

 

A1

B1

M1

M1

A1

M1

 

 

M1

 

M1

For both

 

 

Elim

 

 

 

 

For shorts

For trousers

12.

(a)  Cost of tonne of rice is US $ 500

 Shipping cost of rice = 20/100 x US$ 500 = US$ 100

 Transport to Nairobi = 5/100 x US$ 500 = US$ 25

 Custom duty = 10/100 x US$500 = US$ 500 = US$ 50

 Total cost in dollars = 500 + 100 + 50 + 25 = US$ 675

Converting this to ksh = 76.60 x 675 = ksh 51705

(b)  To make profit of 20% he must sell rice at 120% of the cost price per tonne

 Selling price of a tonne of rice = 120/100 x sh 51705

 = ksh 62046

 1 tonne has 1000kg, selling price of 1kg of rice = 62.046

 = sh 62.00

(c)  Total collection = sh 62046 in US dollars this becomes

= Image From EcoleBooks.com  = US$ 793.4271

Actual profit = US$ 793.4271 – 675 = 118.4271

Actual percentage = 118.4271/625 x 100

= 17.545%

 

B1

B1

B1

A1

 

 

B1

 

B1

 

B1

 

B1

 

B1

 

A1

 
  

10

 

15.  Total exp = 600000 + 100000 M1

= Sh. 700000

 Profit = 108000 – 700000

 % profit = 380000 x 100

60000

631/3 % A1

 

3

 

16.  (a) Swiss Franc = 52/1.28 M1

= 40.625 A1

 

 (b) Kenya shillings = 40.625 x 45.21

= 1837 B1

 

3

17.

Let the rates be x% and y% respectively

x x 50000 = 2250

100

y x 45000 = 2250

100

x = 4.5%

y = 5%

 

 

M1

 

M1

 

A1

 
  

03

 

18.

Sitienei – x

Lagat – 1.1x

Rotich – 1.155x

Diff = 1.155x – 1.1x = 0.55x = 110,000

X = 2,000,000

Rotic paid 1.155 x 200,000 = 231000

M1

 

M1

 

A1

 
  

03

 

19.

5000 x 84.15

= sh. 420750

420750 – 289850

= sh. 130900

Amount = 130900 x 100

65.45

= 200,000 Japanese Yen

M1

 

 

 

M1

 

A1

 
  

03

 

20

a.)

 

 

 

 

 

 

 

 

 

 

b.)

 

 

A = 1200000 (1 – 8/100)2

1200000 (0.92)2

= 1,051,680

 

1015680 (1-12/100)4

1015680 (0.88)4

 

= 609098.58

 

 

125/100 x 609098.58

 

= 761373.23

 

761373.23 = 1200000(1- r/100)72

 

(1/ r/100)72 = 0.6344776

 

72/72 log (1- r/100) = -0.1975836/72

 

Log(1- r/100) = 0.0027442173

 

1-r/100 = 0.9937011

 

r/100 = 0.0062988

r = 0.62988 % p.m.

 

M1

 

M1

 

 

M1

 

 

A1

 

 

M1

 

A1

 

 

M1

 

 

 

M1

 

 

M1

 

 

A1

10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Follow thro’ if A1 is missing

 

 

 

 

 

 

 

 

 

 

 

A1 if A above is lost.

 

 

 

 

 

 

 

 

 

21.

50x + 25y = 200

2x + y = 8…….(i)

Image From EcoleBooks.com

 

 

M1

 

 

M1

 

 

M1

 

 

 

A1

 

 

eqn (i)

 

 

 eqn (ii)

 

 

 solving

 

 

 

 both

  

04

 

22.

Yen = 1000 x 105 x 105 + 1260

100 = 111510 Yen

Ksh = 111510 x 63

105 = Ksh. 66906

M1

A1

B1

 
  

03

 

23

 Image From EcoleBooks.com

R.P 240.50 – 22.90

= Sh 217.60

 

 % profit = Image From EcoleBooks.com

 

M1

 

 

 

 

 

M1

 

A1

 
  

3

 

24

 Image From EcoleBooks.com

When x = 5 and y = 8

 Image From EcoleBooks.com

 

B1

 

B1

 

 

 

 

 

 

 

 

B1

 
  

3

 

25

 Image From EcoleBooks.com

M1

 

M1

 

A1

 
  

3

 

 

26.  2x – 3y + 6 =0

  -3y = -2x – 6

  y = 2x + 2

3

When y = 0 x = -3

x = 0 y = 2

∴ Co-ordinate of y – intercept is (0,2)

  ” ” x – intercept is (-3,0)


 CAO = tan-1
2

3

= 33.69o

θ = 180 – 33.69o

= 146.31o

 

27.  Point y (4 + -2, 7 + -1) = (1, 3)

2 2

grad AB = 7 + 1 = 8

  4 + 2 6

grad xy = – ¾

grad xy = – ¾

y – 3 = – ¾

x – 2

y = – ¾ x + 15/4

 

28.  Y = 3x – 1

M =3

M1m2 = -1

M2 = –1/3  

y – 3 = –1/3

x -2

3y – 9 =-x +2

3y = -x + 11

3 3 3

Y = x/3 + 11/3

 

 

29.  Pt T is 1 + 5, 4 + 10 = (-2, 7)

  2 2

grad. of grid xy = 10- 4 = 14 = -7

  -5 -1 -6 3

grad of L2 = 3

7

Take a general pt P(x,y) on L2


y – 7 = 3

  x – 2 7

 7y – 49 = 3x + 6

Image From EcoleBooks.com   7y = 3x + 55

Or y = 3x + 55

 

 

 

 

Image From EcoleBooks.com

30. a, b

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) Name : a kite

 

 

31. (a) Grad of line QP = 4-2 = 2 = -1

  1-3 -2

Grad of line QR = 1

Take a pt Q(1,4) and T(x,y) on line QR

y- 4 = 1

x – 1

y – 4 = x -1

y = x + 3 …..equ. of QR

 

(b) y= x+3 …(i) Equ of QR

y = 3x -7 …(ii) Equ. of Pr

Solving simultaneously ;:

x +3 = 3x -7

  2x = 10

 x = 5

Substituting y = 8

R is the pt (5,8)

Image From EcoleBooks.comImage From EcoleBooks.comImage From EcoleBooks.comImage From EcoleBooks.comImage From EcoleBooks.comImage From EcoleBooks.comImage From EcoleBooks.comImage From EcoleBooks.com

(c) PS = QR = –   =

 

 

Image From EcoleBooks.com OS = + =

 

S is the point (7,6)

 

 

32.  a) Gradient OA = Gradient of CB

   -1 – 0 = – ½

 2 – 0

   Gradient of CB

y – 3 = – ½

   0 – 4

   2y – 6 = 4

2y = 10

   y = 5

 

  b) i) AN = ON – OA = ½ OM – OA

  OM = OA + ½ AB = (2) + ½ (2)

= 3

 AN = ½ 3 – 2 = ½ – 1/3

  = ½ 1 -1

 

ii) NC = OC – ON

= 0 – 3/2 = –3/2

5 ½ ½

 

 

iii) AC = OC – OA = 0 – 2 = 2 -1

5 -1 3

 

 

c) AN = ½ – 1

3

 

NC = 3/21/3

Image From EcoleBooks.com

 4AN = AC  And A is a common point hence A, N, C lie on a straight line.

 

 

33.  a) ∆ ABC line AB = 7 cm and BC = 8 cm.

 Construction of ∡60o

 

(b) AC = 7.6 + 0.1 and

 ∡ ACB = 53 + 1o

 

 

(c) 2 sides bisector 1

Circle drawn radius 4.4. ± 0.1

 

 

(d) Bisect ∡ ACB

 Bisection line to cut the circle to identify P

 ∡ PBC measure ≡

 

 

(a) AB = 7 cm, BC = 8 cm

∡ ABC = 60o

Image From EcoleBooks.com

(b) AC = 7.6 + 0.1 cm

∡ ABC = 53o±0.1

 

 (c) Perpendicular bisectors of any two sides.

Circle drawn

Radius = 4.4.±0.1. cm

 

(d) ∡ ACB bisected

Bisection line drawn to cut circle at P

∡BPC = ∡BAC = 67o


PBC = 88 ± 0.1o

 

34.

Image From EcoleBooks.com

M (1+8, 1+10) = M (4.5, 5.5)

2 2

 

b) AB: 4x – 5y = -1 x 2

  BC: 5x – 2y = 20 x 5

8x – 10y = -2


25x – 10y = 100

-17x = -102

x= 102/17 = 6.0

24 – 5y = -1

5y = -25

Y = 5

B(6,5)

 

x+ 6.0 = 4.5 x = 3

2

y + 5 = 5.5 y = 6

2


D (3,6)

 

 

c)  AB = √ (16 – 1)2 + (5-1)2

√25 + 16

√41 = 6.40 (units)

35.  Mid ordinate

Area = 1.2 (6.2 + 4.3 + 2.6)

 = 15.72


 




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