A man buys 400 twenty rupee shares at a discount of `20%` and receives a return of `12%` on his money. Calculate :
(i) the amount invested by him
(ii) the rate of dividend paid by the company

Answer

To solve the problem step by step, we will calculate the amount invested by the man and the rate of dividend paid by the company.

### Step 1: Determine the nominal value of one share
The nominal value of one share is given as ₹20.

### Step 2: Calculate the discount on one share
The discount is 20% of the nominal value.
\[ \text{Discount} = 20\% \text{ of } 20 = \frac{20}{100} \times 20 = ₹4 \]

### Step 3: Calculate the market value of one share
The market value of one share is the nominal value minus the discount.
\[ \text{Market Value} = \text{Nominal Value} - \text{Discount} = 20 - 4 = ₹16 \]

### Step 4: Calculate the total nominal value of 400 shares
The total nominal value of 400 shares is calculated as follows:
\[ \text{Total Nominal Value} = \text{Number of Shares} \times \text{Nominal Value} = 400 \times 20 = ₹8000 \]

### Step 5: Calculate the amount invested by the man
The amount invested is equal to the market value of 400 shares.
\[ \text{Amount Invested} = \text{Number of Shares} \times \text{Market Value} = 400 \times 16 = ₹6400 \]

### Step 6: Calculate the income from the investment
The return on investment is given as 12%. Thus, the income can be calculated as:
\[ \text{Income} = 12\% \text{ of Amount Invested = } \frac{12}{100} \times 6400 = ₹768 \]

### Step 7: Calculate the rate of dividend paid by the company
The rate of dividend is calculated using the formula:
\[ \text{Rate of Dividend} = \left( \frac{\text{Income}}{\text{Total Nominal Value}} \right) \times 100 \]
Substituting the values:
\[ \text{Rate of Dividend} = \left( \frac{768}{8000} \right) \times 100 = 9.6\% \]

### Final Answers:
(i) The amount invested by him is ₹6400.
(ii) The rate of dividend paid by the company is 9.6%.