Data Ram lends equal sum of money at the same rate of interest to, A and B. The money lends to A becomes twice of the original amount .in just four years at simple interest. While Data Ram lends to B for the first two years at compound interest and for the rest two years at simple interest. If the difference between the amount of A and B after 4 years is ₹ 2750. What is the amount of money that Data Ram lends to each one?

Options

A. ₹ 40000
B. ₹ 6000
C. ₹ 8000
D. ₹ 80000

Answer

To solve the problem step by step, we will break down the information given and calculate the amounts lent to A and B.

### Step 1: Determine the amount lent to A
Data Ram lends money to A, which doubles in 4 years at simple interest.

Let the principal amount lent to A be \( P \).

According to the simple interest formula:
\[ \text{Amount} = P + \text{SI} \]
Where SI (Simple Interest) is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Here, \( R \) is the rate of interest and \( T \) is the time in years.

Since the amount becomes twice the principal in 4 years:
\[ 2P = P + \text{SI} \]
This simplifies to:
\[ P = \text{SI} \]

Substituting for SI:
\[ P = \frac{P \times R \times 4}{100} \]

This implies:
\[ 100 = R \times 4 \implies R = 25\% \]