A certain sum was invested on simple interest for a period of seven years. During the period of the sixth and the seventh years combined, the interest earned was ₹292. If the maturity amount is ₹3,942, then what is the rate percentage of the interest?

Options

A. 5
B. 2
C. 6.25
D. 2.5

Answer

To solve the problem step by step, we need to find the rate percentage of the interest based on the information given.

### Step 1: Understand the given information
- The interest earned during the 6th and 7th years combined is ₹292.
- The maturity amount after 7 years is ₹3,942.

### Step 2: Calculate the total interest earned in 7 years
Since the interest earned in the 6th and 7th years is ₹292, we can find the interest earned in 7 years. The interest earned in 7 years can be calculated as follows:

\[ \text{Interest in 7 years} = \text{Interest in 6th and 7th years} \times \frac{7}{2} \]

Calculating this gives:

\[ \text{Interest in 7 years} = 292 \times \frac{7}{2} = 292 \times 3.5 = 1,022 \]

### Step 3: Calculate the total interest earned
Now, we know the maturity amount (A) and the total interest earned in 7 years (I). The formula for maturity amount is:

\[ A = P + I \]

Where:
- A = Maturity amount (₹3,942)
- P = Principal amount
- I = Total interest earned in 7 years (₹1,022)

Rearranging the formula to find the principal:

\[ P = A - I \]

Substituting the known values:

\[ P = 3,942 - 1,022 = 2,920 \]

### Step 4: Use the simple interest formula to find the rate of interest
The formula for simple interest is:

\[ I = \frac{P \times R \times T}{100} \]

Where:
- I = Total interest (₹1,022)
- P = Principal amount (₹2,920)
- R = Rate of interest (unknown)
- T = Time period (7 years)

Rearranging the formula to solve for R:

\[ R = \frac{I \times 100}{P \times T} \]

Substituting the known values:

\[ R = \frac{1,022 \times 100}{2,920 \times 7} \]

Calculating this gives:

\[ R = \frac{102,200}{20,440} \approx 5 \]

### Step 5: Conclusion
The rate of interest is approximately **5%**.