A sum of Rs 95 amounts to Rs 105 in 3 years at a certain rate of simple interest. In 5 years, at the same rate of interest, what will a sum of Rs 171 amount to:

Options

A. Rs 201
B. Rs 175
C. Rs 215
D. Rs 189

Answer

To solve the problem step by step, let's follow the process of calculating the simple interest and the amount for the given principal.

### Step 1: Calculate the Simple Interest for the First Scenario
We know that:
- Principal (P) = Rs 95
- Amount (A) = Rs 105
- Time (T) = 3 years

First, we calculate the Simple Interest (SI):
\[ SI = A - P \]
\[ SI = 105 - 95 = 10 \text{ Rs} \]

### Step 2: Calculate the Rate of Interest
Using the formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of Interest (in %)
- T = Time (in years)

Substituting the known values:
\[ 10 = \frac{95 \times R \times 3}{100} \]

Now, rearranging to find R:
\[ 10 = \frac{285R}{100} \]
\[ 1000 = 285R \]
\[ R = \frac{1000}{285} \approx 3.51\% \]

### Step 3: Calculate the Simple Interest for the New Principal
Now we have a new principal:
- New Principal (P) = Rs 171
- Time (T) = 5 years

Using the same rate (R) we calculated:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{171 \times \frac{1000}{285} \times 5}{100} \]
\[ SI = \frac{171 \times 1000 \times 5}{28500} \]
\[ SI = \frac{855000}{28500} = 30 \text{ Rs} \]

### Step 4: Calculate the Total Amount
Now, we can find the total amount (A) using:
\[ A = P + SI \]
Substituting the values:
\[ A = 171 + 30 = 201 \text{ Rs} \]

### Conclusion
Thus, the amount that Rs 171 will amount to in 5 years at the same rate of interest is **Rs 201**.