What approximate value will come in place of the question mark (?) in the following question?
A sum of Rs. X is invested in a scheme offering simple interest for 2 years at the interest rate of 20 % per annum. A sum of Rs. 2X is invested in the same scheme for 3 years. If the difference between the interest received after respective periods is Rs. 1524, what is the value of 3X?

Options

A. 1905
B. 3810
C. 762
D. 5715

Answer

To solve the problem step by step, we need to calculate the simple interest for both investments and then find the value of \(3X\).

### Step 1: Calculate the Simple Interest for the first investment
The first investment is \(X\) for 2 years at an interest rate of 20% per annum.

The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount
- \(R\) = Rate of interest
- \(T\) = Time in years

For the first investment:
\[ SI_1 = \frac{X \times 20 \times 2}{100} = \frac{40X}{100} = 0.4X \]

### Step 2: Calculate the Simple Interest for the second investment
The second investment is \(2X\) for 3 years at the same interest rate of 20% per annum.

Using the same formula:
\[ SI_2 = \frac{2X \times 20 \times 3}{100} = \frac{120X}{100} = 1.2X \]

### Step 3: Find the difference in interest
According to the problem, the difference between the interest received after respective periods is Rs. 1524. Therefore:
\[ SI_2 - SI_1 = 1524 \]
Substituting the values we calculated:
\[ 1.2X - 0.4X = 1524 \]
This simplifies to:
\[ 0.8X = 1524 \]

### Step 4: Solve for \(X\)
To find \(X\), divide both sides by 0.8:
\[ X = \frac{1524}{0.8} = 1905 \]

### Step 5: Calculate \(3X\)
Now, we need to find the value of \(3X\):
\[ 3X = 3 \times 1905 = 5715 \]

### Final Answer
Thus, the value of \(3X\) is **5715**.

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