Quantitative Methods 2013

Exam Year:2013

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This paper consists of TWO section A and B.
Answer all the questions in section A and any other Four questions from section B, in the spaces provided after each question.Candidates should answer the questions in English.

SECTION A (32 marks)
Answer ALL the questions in this section in the spaces provided.
1. The difference between the ages of two employees in a firm 38 years. The age of the older employee is 3 times that of the younger one.
Determine the age of each of the employees.
(4 marks)

2. A worker’s salary was initially Ksh. 18, 000. It was increased in the ratio 3 : 2.
Calculate the worker’s new salary.
(2 marks)

3. An amount of 15m3 of milk was mixed with 120, 000 cm3 of water.
Determine the volume of the mixture in litres.
(4 marks)

4. A certain amount of money was deposited in a bank account paying 15% compound interest payable annually. This amount accumulated to Ksh.24, 000 after 3 years. Determine the deposited amount of money.
(3 marks)
5. Outline two sources of secondary data.
(2 marks)

6. Zawadi, a car dealer, sold a vehicle to another car dealer called Mary at a profit of 10%. Mary then sold the vehicle to Henry, a customer, at a profit of 5%. Henry paid Ksh. 110, 000 more for the vehicle than Mary.
Determine the price that each of the following people paid for the vehicle;
i) Mary;
ii) Henry.
(4 marks)

7. Distinguish between the terms, independent events and mutually exclusive events, as used in probability theory.
(4 marks)

9. State two types of graphs that may be used to present business data.
(2 marks)
10. A rectangular swimming pool has a length of 4 m, wide of 3 m and a height of 2.5m. its floor and inside walls are to be painted. One litre of paint can cover an area of 2m2. Determine the amount of paint required.
(3 marks)

SECTION B (68 marks)
Answer any FOUR questions in this section in the spaces provided.
All questions carry equal marks.

11. a) Highlight five rules that are followed when drawing graphs for presenting data.
(10 marks)
b) A bucket is 96 cm in diameter at the top, 32 cm in diameter at the bottom and 52 cm deep.
Determine its capacity in litres.
(7 marks)

12. The speed, in words per minute, of 100 printing machines in an organization is shown in the table below;

Speed (Words per minute)——Number of printing (Machines)
60 – 62————-14
63 – 65————-24
66 – 68————-38
69 – 71————-22
72 – 74————-2

a) Calculate the:
i) Average speed per machine;
ii) Standard deviation;
iii) Coefficient of variation.
(9 marks)

b) i) Present the data above using a histogram.

ii) Using the histogram in i) above, estimate the modal speed.
(8 marks)

13. a) Jane invested Ksh. 600, 000 in shares whose par value was Ksh. 10 each. The market price was Ksh. 8 per share. She was paid a dividend of 4%. She later sold the shares at Ksh. 8.60 each.

Determine the:
i) Number of shares that Jane bought;
ii) Cash dividend that she was paid;
iii) Profit she made on sale.
(8 marks)

Calculate the amount of money he:
i) had received as salary’;
ii) Spent on each item.
(9 marks)

14. a) A firm is considering investing in either project X or Y. the returns expected from the two projects are categorized as either good, fair or poor. The following information relates to the projects.

Performance (Ksh. millions)—-probability—-(Ksh. millions)—Probability
Good——90, 000————-0.3————-100, 000———-0.2
Fair——70, 000————-0.6————-80, 000———–0.5
Poor——20, 000————-0.1————-30, 000 ———-0.3

i) Calculate the expected return from each project.

ii) Using the results in i) above, advice the firm on which project to undertake.
(9 marks)

b) Explain the meaning of each of the following terms, as used in business.
i) Gross profit
ii) Net profit
iii) Mark – up
iv) Margin.
(8 marks)

15. a) A road construction job was shared by three firms; A, B and C. firm A had 60 men who worked for 18 days. Firm B had 36 men who worked for 20 days and firm C had 48 men who worked for 30 days. The total amount paid for the job was Ksh. 342, 000,000.
The amount paid was to be shared by the three firms in the ratio of their total labour days.
Calculate the payment that each firm received.
(7 marks)
b) Explain five advantages of using interview method in data collection.
(10 m arks)

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