A sum was invested on simple interest at a certain rate for 5 years. If the interest rate is increased by 2%, then the interest increases by Rs 190. What is the sum (in Rs) invested?

Options

A. a)1300
B. b)1600
C. c)1900
D. d)2200

Answer

To solve the problem step by step, we will use the relationship between simple interest, principal amount, rate of interest, and time.

### Step 1: Understand the increase in interest
When the interest rate is increased by 2%, the total interest increases by Rs 190 over 5 years. This means that the additional interest earned due to the increase in the rate is Rs 190.

### Step 2: Calculate the total increase in percentage
Since the interest rate is increased by 2% for 5 years, the total increase in percentage over 5 years is:
\[ \text{Total increase} = 2\% \times 5 = 10\% \]

### Step 3: Relate the increase in interest to the principal
We know that this 10% increase in interest corresponds to Rs 190. Therefore, we can set up the equation:
\[ 10\% \text{ of Principal} = 190 \]

### Step 4: Express the principal in terms of the increase
Let the principal amount be \( P \). Then we can write:
\[ \frac{10}{100} \times P = 190 \]

### Step 5: Solve for the principal
To find \( P \), we can rearrange the equation:
\[ P = 190 \times \frac{100}{10} \]
\[ P = 190 \times 10 \]
\[ P = 1900 \]

### Conclusion
The sum invested is Rs 1900.