A man borrowed Rs 40,000 at 8% simple interest per year. At the end of second year he paid back certain amount and at the end of fifth year he paid back Rs 35960 and cleared the debt. What is the amount that he paid back after the second year?

Options

A. Rs 16200
B. Rs 17400
C. Rs 18600
D. Rs 19200

Answer

To solve the problem step by step, we will first calculate the total interest accrued on the loan over the specified periods and then determine how much was paid back after the second year.

### Step 1: Calculate the total interest for the first two years.

The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times r \times t}{100} \]
Where:
- \( P \) = Principal amount (Rs 40,000)
- \( r \) = Rate of interest (8%)
- \( t \) = Time in years (2 years)

Substituting the values:
\[ SI = \frac{40,000 \times 8 \times 2}{100} \]
\[ SI = \frac{640,000}{100} = 6,400 \]

### Step 2: Calculate the total amount owed after two years.

Total amount after 2 years (Principal + Interest):
\[ \text{Total Amount} = P + SI = 40,000 + 6,400 = 46,400 \]

### Step 3: Determine the amount paid back after the second year.

Let \( x \) be the amount paid back after the second year. The remaining amount after this payment will be:
\[ \text{Remaining Amount} = 46,400 - x \]

### Step 4: Calculate the total interest for the next three years on the remaining amount.

Now, we will calculate the interest for the remaining amount over the next three years (from year 3 to year 5):
- The time \( t \) = 3 years.

Using the same formula for Simple Interest:
\[ SI = \frac{(46,400 - x) \times 8 \times 3}{100} \]
\[ SI = \frac{(46,400 - x) \times 24}{100} = \frac{(46,400 - x) \times 24}{100} \]

### Step 5: Calculate the total amount owed at the end of five years.

Total amount owed at the end of five years:
\[ \text{Total Amount} = \text{Remaining Amount} + \text{Interest for 3 years} \]
\[ = (46,400 - x) + \frac{(46,400 - x) \times 24}{100} \]

### Step 6: Set up the equation with the known final payment.

According to the problem, the man paid Rs 35,960 at the end of the fifth year to clear his debt:
\[ (46,400 - x) + \frac{(46,400 - x) \times 24}{100} = 35,960 \]

### Step 7: Solve the equation.

Let’s simplify the equation:
\[ (46,400 - x) + \frac{(46,400 - x) \times 24}{100} = 35,960 \]
\[ (46,400 - x) \left(1 + \frac{24}{100}\right) = 35,960 \]
\[ (46,400 - x) \left(\frac{124}{100}\right) = 35,960 \]
\[ 46,400 - x = \frac{35,960 \times 100}{124} \]
\[ 46,400 - x = 29,000 \]
\[ x = 46,400 - 29,000 = 17,400 \]

### Conclusion

The amount that he paid back after the second year is Rs 17,400.

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