Jaddu & Ravi invested equal amount at 10% p.a. rate of interest on simple interest & compound interest. Interest received by Ravi after 2 years is same as interest received by Jaddu after some years. Find investment period of Jaddu.

Options

A. 2.8 years
B. None of these
C. 2.4 years
D. 2.1 years

Answer

To solve the problem step by step, we will calculate the simple interest (SI) for Jaddu and the compound interest (CI) for Ravi and set them equal to each other.

### Step 1: Understand the Problem
Jaddu and Ravi both invested the same amount (let's denote it as P) at a rate of 10% per annum. Ravi receives his interest after 2 years using compound interest, while Jaddu receives his interest after an unknown number of years using simple interest. We need to find out how many years Jaddu invested for.

### Step 2: Calculate Interest for Ravi (Compound Interest)
The formula for compound interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^t - P \]
Where:
- \( R = 10\% \)
- \( t = 2 \) years

Substituting the values:
\[ CI = P \left(1 + \frac{10}{100}\right)^2 - P \]
\[ CI = P \left(1 + 0.1\right)^2 - P \]
\[ CI = P \left(1.1\right)^2 - P \]
\[ CI = P \left(1.21\right) - P \]
\[ CI = 1.21P - P \]
\[ CI = 0.21P \]

### Step 3: Calculate Interest for Jaddu (Simple Interest)
The formula for simple interest is:
\[ SI = \frac{P \cdot R \cdot t}{100} \]
Where:
- \( R = 10\% \)
- \( t = T \) (the unknown time period for Jaddu)

Substituting the values:
\[ SI = \frac{P \cdot 10 \cdot T}{100} \]
\[ SI = \frac{PT}{10} \]

### Step 4: Set the Interests Equal
According to the problem, the interest received by Ravi after 2 years is the same as the interest received by Jaddu after T years. Therefore, we can set the two equations equal to each other:
\[ 0.21P = \frac{PT}{10} \]

### Step 5: Simplify the Equation
Since both sides have \( P \) (the principal amount), we can cancel it out:
\[ 0.21 = \frac{T}{10} \]

### Step 6: Solve for T
To find T, we multiply both sides by 10:
\[ T = 0.21 \times 10 \]
\[ T = 2.1 \]

### Conclusion
The investment period of Jaddu is 2.1 years.