Veer invested Rs 22500 for 2 year at the Rate of r% in scheme A at compound interest annually and gets a total amount of Rs 32400 If he added Rs 2600 in this amount and invested total amount in scheme B at S.I, for 3 year at same rate. Then find the total simple interest veer gets from scheme B?

Options

A. Rs 22500
B. Rs 22000
C. Rs 17500
D. Rs. 21000

Answer

To solve the problem step by step, we will follow the process outlined in the video transcript while ensuring clarity in each step.

### Step 1: Determine the Rate of Interest (r%)
Veer invested Rs 22,500 for 2 years at compound interest and received a total amount of Rs 32,400. We can use the formula for compound interest:

\[ A = P \left(1 + \frac{r}{100}\right)^t \]

Where:
- \( A \) = Total amount after time \( t \)
- \( P \) = Principal amount (initial investment)
- \( r \) = Rate of interest per annum
- \( t \) = Time in years

Substituting the known values:

\[ 32,400 = 22,500 \left(1 + \frac{r}{100}\right)^2 \]

### Step 2: Simplify the Equation
To simplify, divide both sides by 22,500:

\[ \frac{32,400}{22,500} = \left(1 + \frac{r}{100}\right)^2 \]

Calculating the left side:

\[ \frac{32,400}{22,500} = 1.44 \]

Thus, we have:

\[ 1.44 = \left(1 + \frac{r}{100}\right)^2 \]

### Step 3: Take the Square Root
Taking the square root of both sides gives:

\[ \sqrt{1.44} = 1 + \frac{r}{100} \]

Calculating the square root:

\[ 1.2 = 1 + \frac{r}{100} \]

### Step 4: Solve for r
Subtract 1 from both sides:

\[ 0.2 = \frac{r}{100} \]

Multiplying both sides by 100:

\[ r = 20\% \]

### Step 5: Calculate the Total Amount for Scheme B
Veer adds Rs 2,600 to the total amount received from Scheme A. The total amount now is:

\[ 32,400 + 2,600 = 35,000 \]

### Step 6: Calculate Simple Interest for Scheme B
Now, Veer invests Rs 35,000 in Scheme B at a simple interest rate of 20% for 3 years. The formula for simple interest (SI) is:

\[ SI = \frac{P \times r \times t}{100} \]

Substituting the values:

\[ SI = \frac{35,000 \times 20 \times 3}{100} \]

### Step 7: Simplify the Calculation
Calculating the SI:

\[ SI = \frac{35,000 \times 60}{100} = \frac{2,100,000}{100} = 21,000 \]

### Final Answer
The total simple interest Veer gets from Scheme B is **Rs 21,000**.

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