If simple interest is 25 for 7th year and CI is 55 for 2 years at certain rate of interest on some amount then find rate of interest?

Options

A. ₹ 20%
B. ₹ 25%
C. ₹ 30%
D. ₹ 15%

Answer

To find the rate of interest based on the given information, we can follow these steps:

### Step 1: Understand the given information
We know that the simple interest (SI) for the 7th year is 25, and the compound interest (CI) for 2 years is 55.

### Step 2: Calculate the interest for the first year
Since the simple interest for the 7th year is the same as the interest for the first year, we can conclude that the interest for the first year (SI) is also 25.

### Step 3: Calculate the compound interest for the second year
The total compound interest for 2 years is given as 55. The interest for the first year is 25, so we can find the interest for the second year (CI for the second year) by subtracting the first year's interest from the total CI:
\[ \text{CI for 2nd year} = \text{Total CI} - \text{SI for 1st year} = 55 - 25 = 30 \]

### Step 4: Relate the second year's CI to the first year's SI
The difference between the interest earned in the second year and the first year can be attributed to the interest on the interest earned in the first year. Therefore, we can say:
\[ \text{CI for 2nd year} = \text{SI for 1st year} \times \frac{r}{100} \]
Where \( r \) is the rate of interest.

### Step 5: Set up the equation
From the above relationship, we can set up the equation:
\[ 30 = 25 \times \frac{r}{100} \]

### Step 6: Solve for \( r \)
To find \( r \), we can rearrange the equation:
\[ \frac{r}{100} = \frac{30}{25} \]
\[ r = \frac{30 \times 100}{25} \]
\[ r = 120 \]
\[ r = 20\% \]

### Conclusion
The rate of interest is 20%.

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