1)Mr Ngate is a consultant with Mitsumi computer garages.At the end of the first month,his basic salary was Ksh 88400 and his monthly basic salary the last month of the h contract was Ksh 117800.By the end of the contract,he had earned a total salary of Ksh 824800.Given that the annual increment rate was constant;
a)Calculate, the period that the contract lasted
b)His monthly increment
c)Mr Ngate's contract extended after the period in (a) above for further four months.In this extension,his monthly basic salary was increased by 4% every month.Determine the total salary that he earned by the end of the year. Give your answer to the nearest 1 shilling
2)A cylindrical water reservoir is served with three pumps,P,Q and R.Pump P can fill the empty reservoir in S hours while Pump Q can fill the same reservoir in 10 hours. When full ,pump Q can drain the reservoir in 3 hours;
a)One day the reservoir was empty and pumps P and Q opened at 8:45am.At 11:15am,pump P developed an electrical fault.Pump Q continued operating alone till the reservoir was full.Find the time of the day that the reservoir was completely from filled.
b)On another day,the reservoir was halfway filled with water. Pump P and R were then opened at the same time.How long did it take to completely drain the reservoir.
c)The reservoir dimensions are base diameter 14metres and height 12.5metres.The water in (b) above is filled in a water tanker of capacity 12000 litres,How many trips does the tanker make to drain the reservoir?
a) To find the period that the contract lasted, we need to find the number of months between the first month and the last month.
Number of months = (Total salary earned - First month's basic salary) / (Annual increment rate * 12)
Number of months = (824800 - 88400) / (117800 - 88400) * 12
Number of months = 736400 / 29400 * 12
Number of months = 24
Therefore, the contract lasted for 24 months.
b) To find the monthly increment, we need to find the difference between the last month's basic salary and the first month's basic salary, and then divide that by the number of months.
Monthly increment = (Last month's basic salary - First month's basic salary) / Number of months
Monthly increment = (117800 - 88400) / 24
Monthly increment = 29400 / 24
Monthly increment = 1225
Therefore, the monthly increment is Ksh 1225.
c) To find the total salary earned by the end of the year, we need to calculate the salary earned in the extension period and add it to the total salary earned during the initial contract period.
Salary earned in extension period = (Last month's basic salary + Monthly increment * 4%) * 4
Salary earned in extension period = (117800 + 1225 * 0.04) * 4
Salary earned in extension period = (117800 + 49) * 4
Salary earned in extension period = 118849 * 4
Salary earned in extension period = 475396
Total salary earned by the end of the year = Total salary earned during initial contract period + Salary earned in extension period
Total salary earned by the end of the year = 824800 + 475396
Total salary earned by the end of the year = 1302196
Therefore, Mr Ngate earned a total salary of Ksh 1302196 by the end of the year.