Anand deposited Rs 6000 on simple interest. He withdraw Rs 4000 and its interest from that amount after 2 years. After next 3 years, he withdraw the rest of the amount and its interest accrued till that time. In all he obtained Rs 900 as interest. The rate of interest per annum was

Options

A. `3%`
B. `4%`
C. `5%`
D. `6%`

Answer

To solve the problem step by step, we will first identify the key information and then calculate the rate of interest per annum.

### Step 1: Identify the total principal amount and the interest earned
Anand deposited a total of Rs 6000. The total interest earned after all withdrawals is Rs 900.

### Step 2: Calculate the interest for the first 2 years
Let's denote the rate of interest per annum as \( r \% \).

The formula for simple interest is:
\[ \text{Simple Interest} = \frac{P \times r \times t}{100} \]
where:
- \( P \) = Principal amount
- \( r \) = Rate of interest per annum
- \( t \) = Time in years

For the first 2 years, the principal amount is Rs 6000:
\[ \text{Interest for 2 years} = \frac{6000 \times r \times 2}{100} = \frac{12000r}{100} = 120r \]

### Step 3: Withdraw Rs 4000 and its interest after 2 years
After 2 years, Anand withdraws Rs 4000 along with the interest earned on it:
\[ \text{Total amount withdrawn} = 4000 + 120r \]

### Step 4: Calculate the remaining amount
The remaining amount after the withdrawal is:
\[ \text{Remaining amount} = 6000 - 4000 = 2000 \]

### Step 5: Calculate the interest on the remaining amount for the next 3 years
The remaining amount of Rs 2000 will earn interest for the next 3 years:
\[ \text{Interest for 3 years on Rs 2000} = \frac{2000 \times r \times 3}{100} = \frac{6000r}{100} = 60r \]

### Step 6: Total interest earned
The total interest earned after 5 years (2 years + 3 years) is:
\[ \text{Total Interest} = 120r + 60r = 180r \]
According to the problem, this total interest equals Rs 900:
\[ 180r = 900 \]

### Step 7: Solve for \( r \)
Now, we can solve for \( r \):
\[ r = \frac{900}{180} = 5 \]

### Conclusion
The rate of interest per annum is \( \boxed{5\%} \).