A man bought 500 shares, each of face value `10rs` of a certain business concern and during the first year after purchase, receives `400rs` as dividend on his shares. Find the rate of dividend on the shares.

Answer

To find the rate of dividend on the shares, we can follow these steps:

### Step 1: Identify the given values
- Number of shares (N) = 500
- Face value of each share (FV) = ₹10
- Total dividend received (D) = ₹400

### Step 2: Write the formula for dividend
The formula for calculating the dividend is:
\[ D = N \times FV \times \left(\frac{R}{100}\right) \]
where:
- \(D\) = Total dividend received
- \(N\) = Number of shares
- \(FV\) = Face value of each share
- \(R\) = Rate of dividend (in percentage)

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula:
\[ 400 = 500 \times 10 \times \left(\frac{R}{100}\right) \]

### Step 4: Simplify the equation
First, calculate \(500 \times 10\):
\[ 500 \times 10 = 5000 \]
Now, substitute this back into the equation:
\[ 400 = 5000 \times \left(\frac{R}{100}\right) \]

### Step 5: Solve for \(R\)
To isolate \(R\), multiply both sides by 100:
\[ 400 \times 100 = 5000 \times R \]
\[ 40000 = 5000 \times R \]
Now, divide both sides by 5000:
\[ R = \frac{40000}{5000} \]
\[ R = 8 \]

### Step 6: State the rate of dividend
The rate of dividend is \(8\%\).

### Final Answer
The rate of dividend on the shares is **8%**.

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