Girija invested a certain amount at the rate of 12 p.c. p.a. for 6 years to obtain an amount of Rs. 34.400. How much amount did Girija obtain as simple interest?

Options

A. Rs.14 .400
B. Rs.12,400
C. Rs. 15,400
D. Data inadequate.

Answer

To find out how much amount Girija obtained as simple interest, we can follow these steps:

### Step 1: Understand the formulas
We need to use the formulas for Simple Interest (SI) and the total Amount (A):
1. Simple Interest (SI) = \( \frac{P \times R \times T}{100} \)
2. Amount (A) = Principal (P) + Simple Interest (SI)

### Step 2: Identify the given values
From the question, we have:
- Rate of Interest (R) = 12% per annum
- Time (T) = 6 years
- Amount (A) = Rs. 34,400

### Step 3: Rearrange the Amount formula
We can rearrange the Amount formula to express Principal (P) in terms of Simple Interest (SI):
\[ A = P + SI \]
So, we can write:
\[ P = A - SI \]

### Step 4: Substitute the values into the SI formula
We can substitute \( P \) from the rearranged formula into the SI formula:
\[ SI = \frac{(A - SI) \times R \times T}{100} \]
Substituting the known values:
\[ SI = \frac{(34400 - SI) \times 12 \times 6}{100} \]

### Step 5: Simplify the equation
First, calculate \( 12 \times 6 = 72 \):
\[ SI = \frac{(34400 - SI) \times 72}{100} \]
Now, multiply both sides by 100 to eliminate the fraction:
\[ 100 \times SI = (34400 - SI) \times 72 \]

### Step 6: Expand and rearrange the equation
Expanding the right side:
\[ 100 \times SI = 34400 \times 72 - SI \times 72 \]
Now, add \( SI \times 72 \) to both sides:
\[ 100 \times SI + 72 \times SI = 34400 \times 72 \]
Combine like terms:
\[ 172 \times SI = 34400 \times 72 \]

### Step 7: Calculate the right side
Now, calculate \( 34400 \times 72 \):
\[ 34400 \times 72 = 2476800 \]
So, we have:
\[ 172 \times SI = 2476800 \]

### Step 8: Solve for SI
Now, divide both sides by 172 to find SI:
\[ SI = \frac{2476800}{172} \]
Calculating this gives:
\[ SI = 14400 \]

### Conclusion
Thus, the amount Girija obtained as simple interest is **Rs. 14,400**.

---