Sure, let’s solve this step by step.
Step 1: Express simple interest [tex]\( I \)[/tex] in terms of [tex]\( P \)[/tex], [tex]\( T \)[/tex], and [tex]\( R \)[/tex]
The formula for simple interest (SI) is:
[tex]\[ I = \frac{P \times R \times T}{100} \][/tex]
Where:
- [tex]\( I \)[/tex] is the simple interest
- [tex]\( P \)[/tex] is the principal amount
- [tex]\( R \)[/tex] is the interest rate per year
- [tex]\( T \)[/tex] is the time period in years
Step 2: Find the interest rate
Given:
- Principal [tex]\( P = \)[/tex] Rs. 20,000
- Time [tex]\( T = \)[/tex] 2 years
- Simple Interest [tex]\( I = \)[/tex] Rs. 7,200
Using the formula:
[tex]\[ I = \frac{P \times R \times T}{100} \][/tex]
We can rearrange this formula to solve for [tex]\( R \)[/tex]:
[tex]\[ R = \frac{I \times 100}{P \times T} \][/tex]
Substituting the given values:
[tex]\[ R = \frac{7200 \times 100}{20000 \times 2} \][/tex]
[tex]\[ R = \frac{720000}{40000} \][/tex]
[tex]\[ R = 18 \][/tex]
Therefore, the interest rate [tex]\( R \)[/tex] is 18%.
Step 3: Divide interest into two parts in the ratio of 1:2
We need to divide the simple interest [tex]\( I = \)[/tex] Rs. 7,200 into two parts such that the ratio between the parts is 1:2.
Let’s denote the two parts as [tex]\( I_1 \)[/tex] and [tex]\( I_2 \)[/tex].
The ratio is 1:2, meaning:
[tex]\[ \frac{I_1}{I_2} = \frac{1}{2} \][/tex]
This implies:
[tex]\[ I_1 = \frac{1}{3} \times I \][/tex]
[tex]\[ I_2 = \frac{2}{3} \times I \][/tex]
Substituting the value of [tex]\( I \)[/tex]:
[tex]\[ I_1 = \frac{1}{3} \times 7200 \][/tex]
[tex]\[ I = 2400 \][/tex]
[tex]\[ I_2 = \frac{2}{3} \times 7200 \][/tex]
[tex]\[ I_2 = 4800 \][/tex]
Therefore, the two parts of the interest are Rs. 2,400 and Rs. 4,800.
Summary:
i. The formula for simple interest is [tex]\( I = \frac{P \times R \times T}{100} \)[/tex].
ii. The interest rate is 18%.
iii. The interest can be divided into two parts: Rs. 2,400 and Rs. 4,800, in the ratio of 1:2.
