Find the income derived from 44 shares of rs 25 each at 5 premium (brokerage 1/4 per share)the rate of dividend being `5%` . Also find the rate of interest on the investement.

Options

A. Rs 60.5 , `4.55%`
B. `Rs 60.5%`
C. `Rs80.5 , 5.55%`
D. none of these

Answer

To solve the problem step by step, let's break it down into manageable parts.

### Step 1: Calculate the cost of one share
The cost of one share includes the face value, the premium, and the brokerage.

- Face value of one share = Rs 25
- Premium = Rs 5
- Brokerage = Rs 0.25 (which is 1/4 of a rupee)

**Cost of one share = Face value + Premium + Brokerage**
\[ \text{Cost of one share} = 25 + 5 + 0.25 = 30.25 \]

### Step 2: Calculate the total cost for 44 shares
Now, we need to find the total cost for 44 shares.

**Total cost = Cost of one share × Number of shares**
\[ \text{Total cost} = 30.25 \times 44 = 1331 \]

### Step 3: Calculate the income from dividends
The rate of dividend is given as 5%. The income from dividends can be calculated using the formula:

**Income from dividends = (Total face value of shares) × (Rate of dividend)**
- Face value of one share = Rs 25
- Total face value for 44 shares = 25 × 44 = Rs 1100

Now, calculate the income from dividends:
\[ \text{Income from dividends} = 1100 \times \frac{5}{100} = 55 \]

### Step 4: Calculate the rate of interest on the investment
The rate of interest can be calculated using the formula:

**Rate of interest = (Income from dividends / Total cost) × 100**
\[ \text{Rate of interest} = \left( \frac{55}{1331} \right) \times 100 \approx 4.13\% \]

### Summary of Results
- Total cost of 44 shares = Rs 1331
- Income from dividends = Rs 55
- Rate of interest on the investment ≈ 4.13%