A sum of Rs 8,500 amounts to Rs 11,900 in 5 years at simple interest per annum. If the rate of interest is increased by 3%. Then the increased amount for the same period is:

Options

A. Rs 12,175
B. Rs 13,175
C. Rs 12,475
D. Rs 13,275

Answer

To solve the problem step by step, we will follow the process of calculating the simple interest and then the new amount after increasing the rate of interest.

### Step 1: Calculate the Simple Interest (SI)
We know that:
- Principal (P) = Rs. 8,500
- Amount (A) = Rs. 11,900
- Time (T) = 5 years

Using the formula for the amount in simple interest:
\[ A = P + SI \]
We can rearrange it to find the Simple Interest (SI):
\[ SI = A - P \]
Substituting the values:
\[ SI = 11,900 - 8,500 = 3,400 \]

### Step 2: Calculate the Rate of Interest (R)
Now, we can use the formula for Simple Interest to find the rate of interest:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 3,400 = \frac{8,500 \times R \times 5}{100} \]
Rearranging to find R:
\[ R = \frac{3,400 \times 100}{8,500 \times 5} \]
Calculating the right side:
\[ R = \frac{340,000}{42,500} = 8\% \]

### Step 3: Increase the Rate of Interest
The problem states that the rate of interest is increased by 3%. Therefore, the new rate of interest (R1) is:
\[ R1 = R + 3 = 8 + 3 = 11\% \]

### Step 4: Calculate the New Simple Interest (SI1)
Using the new rate of interest, we can calculate the new simple interest for the same principal and time:
\[ SI1 = \frac{P \times R1 \times T}{100} \]
Substituting the values:
\[ SI1 = \frac{8,500 \times 11 \times 5}{100} \]
Calculating:
\[ SI1 = \frac{8,500 \times 55}{100} = 4,675 \]

### Step 5: Calculate the New Amount (A1)
Now, we can find the new amount (A1) using the new simple interest:
\[ A1 = P + SI1 \]
Substituting the values:
\[ A1 = 8,500 + 4,675 = 13,175 \]

### Final Answer
The increased amount for the same period is Rs. **13,175**.

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