Brinda borrowed Rs. 1000 to build a hut. She pays 5% simple interest . She lets the hut to Ramu and receives the rent of Rs. `12(1)/(2)` per month from Ramu. In how many years Brinda ought to clear off the debt ?

Answer

To solve the problem step by step, we need to calculate how long it will take Brinda to pay off her debt using the rent she receives from Ramu.

### Step 1: Calculate the Simple Interest
Brinda borrowed Rs. 1000 at a simple interest rate of 5% per annum.

The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (Rs. 1000)
- \( R \) = Rate of interest (5%)
- \( T \) = Time in years

### Step 2: Calculate the Total Amount to be Paid
The total amount (A) to be paid after T years is given by:
\[ A = P + SI \]
Substituting the formula for SI, we get:
\[ A = P + \frac{P \times R \times T}{100} \]
This can be simplified to:
\[ A = P \left(1 + \frac{R \times T}{100}\right) \]

### Step 3: Calculate the Monthly Rent
Brinda receives Rs. 12.5 per month from Ramu. To find out how much she earns in a year, we multiply the monthly rent by 12:
\[ \text{Annual Rent} = 12.5 \times 12 = Rs. 150 \]

### Step 4: Set Up the Equation
Now, we need to find out how many years (T) it will take for the total rent received to equal the total amount to be paid. Thus, we set the annual rent equal to the simple interest accrued:
\[ 150 \times T = \frac{1000 \times 5 \times T}{100} \]

### Step 5: Simplify the Equation
This simplifies to:
\[ 150T = 50T \]
Now, we can rearrange this equation to isolate T:
\[ 150T - 50T = 0 \]
\[ 100T = 0 \]
This implies:
\[ T = 10 \]

### Conclusion
Brinda ought to clear off her debt in **10 years**.

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