A sum of Rs. x was invested at 10% simple interest for 3 years. If the same sum was invested at 4% more for same period, then it would have fetched Rs. 120 more. Find the value of 5x. (in Rs.)

Options

A. 5000
B. 4800
C. 3600
D. 5500

Answer

To solve the problem step by step, we will follow the logic provided in the video transcript.

### Step 1: Understand the given information
We have a principal amount \( x \) which is invested at 10% simple interest for 3 years. When the interest rate is increased by 4% (making it 14%), the interest earned is Rs. 120 more than the interest earned at 10%.

### Step 2: Calculate the interest earned at 10%
The formula for simple interest is:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

For the first investment at 10% for 3 years:
\[ \text{SI}_{10\%} = \frac{x \times 10 \times 3}{100} = \frac{30x}{100} = 0.3x \]

### Step 3: Calculate the interest earned at 14%
For the second investment at 14% for 3 years:
\[ \text{SI}_{14\%} = \frac{x \times 14 \times 3}{100} = \frac{42x}{100} = 0.42x \]

### Step 4: Set up the equation based on the difference in interest
According to the problem, the difference in interest earned from the two rates is Rs. 120:
\[ \text{SI}_{14\%} - \text{SI}_{10\%} = 120 \]
Substituting the values we found:
\[ 0.42x - 0.3x = 120 \]
\[ 0.12x = 120 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 0.12:
\[ x = \frac{120}{0.12} = 1000 \]

### Step 6: Find the value of \( 5x \)
Now, we need to find \( 5x \):
\[ 5x = 5 \times 1000 = 5000 \]

### Final Answer
The value of \( 5x \) is Rs. 5000.

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