A certain sum of money amounts to Rs. 918 in 2 years and Rs. 969 in 3.5 years at simple interest. What is the rate of interest (in % per annum)?

Options

A. 4
B. 5
C. 6
D. 8

Answer

To solve the problem step by step, we will follow the logical reasoning presented in the video transcript.

### Step 1: Identify the amounts and time periods
We know:
- Amount A (after 2 years) = Rs. 918
- Amount B (after 3.5 years) = Rs. 969

### Step 2: Calculate the difference between the two amounts
The difference between the two amounts is:
\[ \text{Difference} = 969 - 918 = Rs. 51 \]

### Step 3: Determine the time difference
The time difference between the two amounts is:
\[ \text{Time difference} = 3.5 \text{ years} - 2 \text{ years} = 1.5 \text{ years} \]

### Step 4: Calculate the simple interest for the time difference
The Rs. 51 that we calculated is the simple interest earned over the 1.5 years.

### Step 5: Calculate the simple interest per year
To find the simple interest for 1 year, we divide the total simple interest by the time period:
\[ \text{Simple Interest per year} = \frac{51}{1.5} = Rs. 34 \]

### Step 6: Calculate the total simple interest for 2 years
Now, we can find the total simple interest for 2 years:
\[ \text{Total Simple Interest for 2 years} = 34 \times 2 = Rs. 68 \]

### Step 7: Calculate the principal amount
Using the amount after 2 years, we can find the principal amount (P):
\[ \text{Principal} = \text{Amount} - \text{Simple Interest} \]
\[ P = 918 - 68 = Rs. 850 \]

### Step 8: Use the simple interest formula to find the rate
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest
- T = Time in years

Using the values we have:
\[ 68 = \frac{850 \times R \times 2}{100} \]

### Step 9: Solve for R
Rearranging the equation to solve for R:
\[ 68 = \frac{1700R}{100} \]
\[ 68 = 17R \]
\[ R = \frac{68}{17} = 4\% \]

### Final Answer
The rate of interest is **4% per annum**.

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