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Cbm 03: Business Mathematics Question Paper
Cbm 03: Business Mathematics
Course:Certificate In Business Management
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
EXAMINATION FOR THE AWARD OF
CERTIFICATE IN BUSINESS MANAGEMENT
CBM 03: BUSINESS MATHEMATICS
STREAMS: CERT (BM) TIME: 2 HOURS
DAY/DATE: THURSDAY 8/8/2013 8.30 PM – 10.30 AM
INSTRUCTIONS:
Answer Question ONE and any other TWO Questions
Do not write on this Question Paper
QUESTION ONE (30 Marks)
(a) Give five methods of data collection. [5 Marks]
(b) A random sample of 280 managers, are asked to give their opinion of their firms prospects for the coming year. The firms are classified as small, medium and larger. The prospects are classified as declining, remaining the same, and improving. A total of 130, 60 and 90 firms are small, medium and large respectively. The number of firms considered to be declining, remaining the same and improving have 40, 100 and 140 respectively. The prospects are that 20 small, 10 medium firms will decline, while 50 small firms have a prospect of improving, only 20 medium and 20 large firms have a prospect of remaining the same.
Required.
Summarize the above information in a tabular form. [10 Marks]
(c) Calculate the Harmonic mean for the data given 20km/h, 30km/h, 40km/hr, 45km/h and 50km/h [5 Marks]
(d) Given the following data 20, 28, 40, 12, 30, 15, 50
(i) Find the first quartile [3 Marks]
(ii) Find the third quartile [3 Marks]
(iii) Find the semi-interquartile range of the data. [2 Marks]
(e) Name any two allowable deductions in taxation. [2 Marks]
QUESTION TWO
(a) The salaries to employees of two companies Y and X are distributed as follows
Range of income (Sh 000) No of employees
Company Y Company X
4 – 6 5 15
6 – 8 7 30
8 – 10 7 28
10 – 12 18 24
12 – 14 23 17
14 – 16 14 4
16 – 18 10 12
18 – 20 16 2
20 - 22 _4__ _2__
104
==== 134
====
Required:
(a) The mean and standard deviation of company Y employees. [8 Marks]
(b) The mean and standard deviation of company x employees [8 Marks]
(c) The coefficient of variation of the salaries of the two companies. [4 Marks]
QUESTION THREE
(a) John Karanja intends to buy a washing machine for her dry cleaning business on hire purchase terms, the cash price of the washing machine is sh 84,000. The hire purchase terms comprise 24 monthly installments of sh 3,500 each and 1 ½ percent monthly interest on the unpaid amount.
Required:
(i) The total amount of the 24 installments. [2 Marks]
(ii) The total amount of money John will pay for the washing machine under hire purchase terms. [2 Marks]
(b) Mwana Mali invested shs 15,000 and shs 20,000 at a simple interest rates of r percent per annum and t percent per annum respectively. The investment earned him a total of shs 11,400 after a period of 3 years. If Mwana Mali had invested shs 35,000 at a simple interest of ((r+t)/2)
Percent per annum the investment would have earned him a total of sh 11,550 after a period of 3 years.
Required:
(i) The rates of interest represented by r percent and t percent. [10 Marks]
(ii) The total interest that Mwana Mali would have earned if he invested sh 35,000 for 3 years at the interest rate of r percent compounded semi annually. [3 Marks]
(c) A fair coin is tossed twice. Determine the probability having
(i) Exactly 2 leads [1 Mark]
(ii) Exactly I tail [1 Mark]
(iii) Exactly 2 tails [1 Mark]
QUESTION FOUR
(a) Juma a casual employee is paid shs. 300 per hour for normal working hours from Monday to Friday. The normal working hours start at 8.00 am and end at 5.00 pm excluding a one hour lunch break. For any work done outside the normal working hours Juma is paid ksh. 500 per hour. The wages are paid at the end of the month and are subject to income tax deductions calculated according to the following schedule.
Monthly taxable pay (Ksh) Rate of Tax
1 – 10164 10%
10165 – 19740 15%
19741 – 29316 20%
29317 – 38892 25%
Excess over 38892 30%
Pasmal relief is Ksh 1,162 per month
Required:
The net pay for Juma for the month of April 2008 given that in addition to normal working hours he worked 20 hours overtime within the month (assume a 4 week month) [10 Marks]
(b) Mr. Kochi is a businessman. In the month of August 2009 he travelled to Dubai on a business trip. He had saved sh 1,500,000 for a trip. He bought a return ticket for us $440 in Kenya. On arrival in Dubai he converted all his currency to US dollars. He stayed in Dubai for five days and spent us $ 100 per day on accommodation. He also spent US $ 40 per day on food and other basic requirements. He bought a second hand vehicle for a Japanese friend for 564,000 Japanese yen. He also bought some English jewellary for his wife worth starling pounds 250. On return to Kenya he paid import duty for the vehicle and jewellery at 35% of the cost exclusive shipping charges. He had paid US$ 560 in Dubai as shipping charges for the vehicle. Further he paid 16% VAT for the vehicle which was charged on the cost including import duty. Port clearance took seven days and the port charged a storage fee of shs 1500 per day.
Required:
The total amount of money in Kenya Shillings Mr. Kochi was left with after clearing all the port charges [10 Marks]
NB:
1 US dollar = Ksh 78
I starling Pound = Ksh 120
100 Japanese Yen = Ksh 62
QUESTION FIVE
(a) The selling price of a sewing machine is sh 20,500, if bought for cash, a discount of 15% is given on the selling price. The hire purchase terms comprise of a deposit of 30%on the selling price and 12 monthly installments of Ksh 1,950 each.
Required:
(i) The cash price of the sewing machine. [2 Marks]
(ii) The hire purchase of the sewing machine. [3 Marks]
(iii) The difference in price between cash and buying in the hire purchase terms.
[2 Marks]
(iv) Percentage increase of the hire purchase price over the selling price.
[3 Marks]
(b) State the general rules that may be followed when constructing a table for a given information. [10 Marks]
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