Rakesh invests ₹12000 as fixed deposit at a bank at the rate of 10% per annum SI. But due to some pressing needs he has to withdraw the entire money after 3 years. for which the bank allowed him a lower rate of interest. If he gets ₹3320 less than what he would have got at the end of 5 years. the rate of interest allowed by the bank is

Options

A. 68/9%
B. 64/9%
C. 67/9%
D. 61/9%

Explanation

To solve the problem step-by-step, we will calculate the amount Rakesh would have received at the end of 5 years and then find out the interest he received after 3 years. Finally, we will determine the lower rate of interest allowed by the bank.

### Step 1: Calculate the amount Rakesh would have received after 5 years at 10% per annum SI.

**Formula for Simple Interest (SI):**
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (₹12000)
- \( R \) = Rate of interest (10%)
- \( T \) = Time (5 years)

**Calculation:**
\[ \text{SI} = \frac{12000 \times 10 \times 5}{100} \]
\[ \text{SI} = \frac{1200000}{100} = 12000 \]

**Total Amount after 5 years:**
\[ \text{Total Amount} = P + \text{SI} = 12000 + 12000 = 24000 \]

### Step 2: Calculate the amount Rakesh received after 3 years.

Since he received ₹3320 less than what he would have received after 5 years:
\[ \text{Amount after 3 years} = 24000 - 3320 = 20680 \]

### Step 3: Calculate the interest Rakesh received after 3 years.

**Total Amount after 3 years:**
\[ \text{Total Amount} = P + \text{SI} \]
Let the interest received after 3 years be \( \text{SI}_3 \).
\[ 20680 = 12000 + \text{SI}_3 \]
\[ \text{SI}_3 = 20680 - 12000 = 8680 \]

### Step 4: Use the SI formula to find the lower rate of interest.

Using the formula for Simple Interest:
\[ \text{SI}_3 = \frac{P \times R' \times T}{100} \]
Where:
- \( R' \) = Rate of interest for 3 years
- \( T \) = 3 years

Substituting the known values:
\[ 8680 = \frac{12000 \times R' \times 3}{100} \]

### Step 5: Solve for \( R' \).

Rearranging the equation:
\[ 8680 = \frac{12000 \times R' \times 3}{100} \]
\[ 8680 \times 100 = 12000 \times R' \times 3 \]
\[ 868000 = 36000 \times R' \]
\[ R' = \frac{868000}{36000} \]
\[ R' = \frac{868}{36} \]
\[ R' = \frac{217}{9} \]

### Step 6: Convert to percentage.

\[ R' \approx 24.11\% \]

### Final Answer:
The rate of interest allowed by the bank is \( \frac{217}{9} \% \) or approximately \( 24.11\% \).

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