A man borrowed Rs. Rs.12000 on compound interest at the rate of 20% per annum and at the end of first year man again borrowed Rs. 'X' more on compound interest at the same rate of interest. If at the end of second year, man paid total amount of Rs.20400, then find value of 'X"?

Options

A. Rs.2400
B. Rs.2000
C. Rs.3600
D. Rs.2600

Answer

To solve the problem step by step, we will calculate the total amount the man has to pay at the end of the second year after borrowing Rs. 12,000 initially and then Rs. X at the end of the first year.

### Step 1: Calculate the total amount after the first year
The man borrowed Rs. 12,000 at a compound interest rate of 20% per annum.

**Interest for the first year:**
\[ \text{Interest} = \frac{P \times R \times T}{100} = \frac{12000 \times 20 \times 1}{100} = \frac{240000}{100} = 2400 \]

**Total Amount after the first year:**
\[ \text{Total Amount} = \text{Principal} + \text{Interest} = 12000 + 2400 = 14400 \]

### Step 2: Calculate the total amount after the second year
At the end of the first year, the man borrows Rs. X. The total amount he has to pay at the end of the second year is Rs. 20,400.

**Total amount after the second year:**
The total amount after the second year will be the amount from the first year plus the amount borrowed in the second year plus the interest on both amounts.

**Interest on Rs. 12,000 for the second year:**
\[ \text{Interest on } 14400 = \frac{14400 \times 20 \times 1}{100} = \frac{288000}{100} = 2880 \]

**Total Amount after the second year (including Rs. X):**
\[ \text{Total Amount} = 14400 + X + \text{Interest on } X \]
The interest on Rs. X for one year at 20% is:
\[ \text{Interest on } X = \frac{X \times 20 \times 1}{100} = \frac{20X}{100} = 0.2X \]

Thus, the total amount after the second year can be expressed as:
\[ 20400 = 14400 + X + 0.2X \]

### Step 3: Simplify the equation
Combining the terms gives:
\[ 20400 = 14400 + 1.2X \]

### Step 4: Solve for X
Subtract 14400 from both sides:
\[ 20400 - 14400 = 1.2X \]
\[ 6000 = 1.2X \]

Now, divide both sides by 1.2:
\[ X = \frac{6000}{1.2} = 5000 \]

### Step 5: Conclusion
The value of X is Rs. 5000.