SOLUTION: A man gets a rise of 10% in salary at the end of his first year of service, and further rises of 20% and 25% at the end of the second and third years respectively,the rise in each

Question 1114522: A man gets a rise of 10% in salary at the end of his first year of service, and further rises of 20% and 25% at the end of the second and third years respectively,the rise in each case being calculated on his salary at the beginning of the year. Find geometric mean.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it's been a while, so i forgot what a geometric mean is.

fortunately there are references on the web that can help.

here's one.

http://www.mathsisfun.com/numbers/geometric-mean.html

based on your description of the problem, you have a series of numbers.

if the first number is x, then:

the second number is 1.1 * x.
the third number is 1.2 * 1.1 * x.
the fourth number is 1.25 * 1.2 * 1.1 * x

this is based on my understanding that each year's increase is based on the salary at the beginning of that year.

the geometric means would therefore be:

the fourth root of (x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x)

this becomes the fourth foot of (1.1^3 * 1.2^2 * 1.25 * x^4).

this becomes equal to the fourth root of (1.1^3 * 1.2^2 * 1.25) * x.

this becomes equal to the fourth root of (2.3958) * x.

this becomes equal to 1.244121056 * x

if this is true, then (1.244121056 * x) ^ 4 must be equal to (x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x)

(1.244121056 * x) ^ 4 is equal to 2.3958 * x^4.

(x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x) is equal to 2.3958 * x^4.

this confirms that the geometric mean has been calculated correctly according to the instructions provided by the referenced website.

RELATED QUESTIONS
A man gets a rise of 10% in salary at the end of his first year of service, and further... (answered by Theo)

a man gets a rise of 10% in salary at the end of his first year of service, and further... (answered by richwmiller)

A man gets a raise of 12% in salary at end of first year and further raises of 16% ,19%... (answered by greenestamps,ikleyn)

1) A man had two employments on the same day with the following salary condition:The... (answered by mananth)

The monthly salary of Mr. Johnson was ₦320,000 for each of the first three years. He... (answered by Edwin McCravy,ikleyn)

4. A man earned $3500 the first year he worked. If he received a raise of $600 at the end (answered by fractalier)

On the first day of the year, a man deposits $1000 in a bank at 8% per year, compounded... (answered by addingup)

Bob has two jobs offers with a starting salary of $100,000 per year and monthly... (answered by scott8148,TimmyT)

.Bob has two job offers with a starting salary of $100,000 per year and monthly... (answered by lynnlo)