How much should a man invest in `50rs` shares selling at `60rs` to obtain an income of `450rs` if the rate of dividend declared is `10%`. Also find his yield percent to the nearest whole number.

Answer

To solve the problem step by step, we will follow the given information and apply the necessary formulas.

### Step 1: Identify the given information
- Nominal value of the share (face value) = ₹50
- Market value of the share = ₹60
- Rate of dividend declared = 10%
- Desired annual income = ₹450

### Step 2: Set up the equation for annual income
The annual income from shares can be calculated using the formula:
\[ \text{Annual Income} = \text{Dividend Rate} \times \text{Nominal Value} \times \text{Number of Shares} \]
Let the number of shares be \( x \).

Substituting the known values into the equation:
\[ 450 = 0.10 \times 50 \times x \]

### Step 3: Solve for the number of shares \( x \)
Rearranging the equation:
\[ 450 = 5x \]
To find \( x \):
\[ x = \frac{450}{5} = 90 \]
So, the man needs to buy 90 shares.

### Step 4: Calculate the total investment
The total investment can be calculated using the formula:
\[ \text{Investment} = \text{Number of Shares} \times \text{Market Value} \]
Substituting the values:
\[ \text{Investment} = 90 \times 60 = 5400 \]
Thus, the man should invest ₹5400.

### Step 5: Calculate the yield percent
Yield percent can be calculated using the formula:
\[ \text{Yield Percent} = \left( \frac{\text{Annual Income}}{\text{Investment}} \right) \times 100 \]
Substituting the values:
\[ \text{Yield Percent} = \left( \frac{450}{5400} \right) \times 100 \]
Calculating this gives:
\[ \text{Yield Percent} = \left( \frac{450}{5400} \right) \times 100 = 8.33\% \]
To the nearest whole number, the yield percent is 8%.

### Final Answers
- The man should invest ₹5400.
- The yield percent to the nearest whole number is 8%.