Sure, let's address both parts of the question step by step.
### 1. Finding the Simple Interest:
To find the simple interest of N 400.00 for 4 years at 6% per annum, we can use the formula for simple interest:
[tex]\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \][/tex]
where [tex]\( P \)[/tex] is the principal amount, [tex]\( R \)[/tex] is the rate of interest per annum, and [tex]\( T \)[/tex] is the time period in years.
Given:
- Principal amount, [tex]\( P = N 400.00 \)[/tex]
- Rate of interest, [tex]\( R = 6\% \)[/tex] per annum
- Time period, [tex]\( T = 4 \)[/tex] years
Substituting the values into the formula:
[tex]\[ SI = \frac{400 \times 6 \times 4}{100} \][/tex]
[tex]\[ SI = \frac{9600}{100} \][/tex]
[tex]\[ SI = N 96.00 \][/tex]
Thus, the simple interest is [tex]\( N 96.00 \)[/tex].
So the correct option is:
(c) [tex]\( N 96.00 \)[/tex]
### 2. Finding the Total Cost of the Business:
Two men shared the cost of a business in the ratio [tex]\( 2:3 \)[/tex]. The smaller share is [tex]\( N 750.00 \)[/tex]. We need to find the total cost of the business.
Firstly, let's understand the ratio:
- Smaller share (2 parts): [tex]\( N 750.00 \)[/tex]
- Larger share (3 parts): Let’s denote it by [tex]\( x \)[/tex]
We start by determining the combined ratios:
[tex]\[ 2 + 3 = 5 \][/tex]
Next, we determine the value of one part of the ratio. Since the smaller share (2 parts) is [tex]\( N 750.00 \)[/tex]:
[tex]\[ \text{Value of one part} = \frac{750.0}{2} = N 375.00 \][/tex]
Now, to find the total cost of the business, we multiply the total number of parts by the value of one part:
[tex]\[ \text{Total cost} = \text{Total parts} \times \text{Value of one part} \][/tex]
[tex]\[ \text{Total cost} = 5 \times 375 \][/tex]
[tex]\[ \text{Total cost} = N 1875.00 \][/tex]
Therefore, the total cost of the business is [tex]\( N 1875.00 \)[/tex].
