To solve the problem step by step, we will calculate the amount the man needs to pay at the end of the third year in order to clear his debt.
### Step 1: Calculate the interest for the first year
The principal amount borrowed is Rs. 10,000, and the rate of interest is 5% per annum.
**Interest for the first year (I1)**:
\[
I_1 = \frac{P \times R \times T}{100}
\]
Where:
- \( P = 10,000 \)
- \( R = 5 \)
- \( T = 1 \)
Calculating:
\[
I_1 = \frac{10,000 \times 5 \times 1}{100} = 500
\]
### Step 2: Calculate the total amount owed at the end of the first year
At the end of the first year, the total amount owed (Principal + Interest) will be:
\[
\text{Total Amount} = P + I_1 = 10,000 + 500 = 10,500
\]
### Step 3: Calculate the repayment at the end of the first year
The man repays 35% of the sum borrowed at the end of the first year:
\[
\text{Repayment} = \frac{35}{100} \times 10,000 = 3,500
\]
### Step 4: Calculate the remaining debt after the first year
Remaining debt after the first year:
\[
\text{Remaining Debt} = \text{Total Amount} - \text{Repayment} = 10,500 - 3,500 = 7,000
\]
### Step 5: Calculate the interest for the second year
Now, we will calculate the interest on the remaining debt for the second year:
\[
I_2 = \frac{7,000 \times 5 \times 1}{100} = 350
\]
### Step 6: Calculate the total amount owed at the end of the second year
Total amount owed at the end of the second year:
\[
\text{Total Amount} = \text{Remaining Debt} + I_2 = 7,000 + 350 = 7,350
\]
### Step 7: Calculate the repayment at the end of the second year
The man repays 42% of the sum borrowed at the end of the second year:
\[
\text{Repayment} = \frac{42}{100} \times 10,000 = 4,200
\]
### Step 8: Calculate the remaining debt after the second year
Remaining debt after the second year:
\[
\text{Remaining Debt} = \text{Total Amount} - \text{Repayment} = 7,350 - 4,200 = 3,150
\]
### Step 9: Calculate the interest for the third year
Now, we will calculate the interest on the remaining debt for the third year:
\[
I_3 = \frac{3,150 \times 5 \times 1}{100} = 157.5
\]
### Step 10: Calculate the total amount owed at the end of the third year
Total amount owed at the end of the third year:
\[
\text{Total Amount} = \text{Remaining Debt} + I_3 = 3,150 + 157.5 = 3,307.5
\]
### Final Step: Calculate the total payment required at the end of the third year
The total amount the man must pay at the end of the third year to clear the debt is:
\[
\text{Total Payment} = \text{Remaining Debt} + I_3 = 3,150 + 157.5 = 3,307.5
\]
Thus, the man must pay **Rs. 3,307.5** at the end of the third year to clear the debt.
