A man’s salary increases by Ghȼ800.00 each
year. If his total salary at the end of 12 years in
Ghȼ1,852,800.00. Find his initial salary in the
twelfth year.
A. Ghȼ15,000,000.00
B. Ghȼ1,500,000.00
C. Ghȼ150,000.00
D. Ghȼ15,000.00
Let the man's initial salary be x.
After one year, his salary will be x + 800.
After two years, his salary will be x + 2(800) = x + 1600.
Similarly, after 12 years, his salary will be x + 12(800) = x + 9600.
We are given that the total salary at the end of 12 years is Ghȼ1,852,800. So, we can write:
x + (x+800) + (x+1600) + ... + (x+9600) = 1,852,800
Simplifying this, we get:
12x + 800(1+2+...+12) = 1,852,800
12x + 800(78) = 1,852,800
12x = 1,852,800 - 62,400
12x = 1,790,400
x = 149,200
Therefore, the man's initial salary in the twelfth year (i.e. after 11 salary increases of Ghȼ800 each) was Ghȼ149,200.
Answer: C. Ghȼ150,000.00
Let's work through this step-by-step:
1. We know that the man's salary increases by Ghȼ800.00 each year.
2. The total salary at the end of 12 years is Ghȼ1,852,800.00.
To find the initial salary in the twelfth year, we need to work backwards.
3. Let X be the initial salary in the twelfth year.
4. The salary in the twelfth year would be X + (12 * Ghȼ800.00).
5. So, X + 12 * Ghȼ800.00 = Ghȼ1,852,800.00.
Now, we can solve for X.
6. Subtracting 12 * Ghȼ800.00 from both sides of the equation, we get X = Ghȼ1,852,800.00 - 12 * Ghȼ800.00.
Calculating the right-hand side of the equation:
7. X = Ghȼ1,852,800.00 - 12 * Ghȼ800.00.
8. X = Ghȼ1,852,800.00 - Ghȼ9,600.00.
9. X = Ghȼ1,843,200.00.
Therefore, the man's initial salary in the twelfth year is Ghȼ1,843,200.00.
Answer: The correct option is B. Ghȼ1,500,000.00