A man invested Rs 9,000 in `3%` (Rs 100) shares at a discount of `10%` He sold all the shares at the rate of Rs 95 each and invested the processed in `4%` (Rs 50) shares at par. Find the change in his income.

Answer

To solve the problem step by step, we will break down the calculations involved in the investment and the changes in income.

### Step 1: Calculate the number of 3% shares purchased
The man invested Rs 9,000 in 3% shares of Rs 100 each at a discount of 10%.

The price of each share after the discount:
\[ \text{Price of each share} = 100 - (10\% \text{ of } 100) = 100 - 10 = 90 \]

Let \( X \) be the number of shares purchased. The total investment can be expressed as:
\[ X \times 90 = 9000 \]

Now, solving for \( X \):
\[ X = \frac{9000}{90} = 100 \]

### Step 2: Calculate the initial income from the 3% shares
The income from the shares is calculated as:
\[ \text{Income} = \text{Number of shares} \times \text{Dividend rate} = 100 \times 3 = 300 \]

### Step 3: Calculate the total amount received from selling the shares
The man sold all his shares at Rs 95 each. Therefore, the total amount received from selling the shares is:
\[ \text{Total amount from sale} = 100 \times 95 = 9500 \]

### Step 4: Calculate the number of 4% shares purchased
Now, he invests the proceeds (Rs 9500) in 4% shares of Rs 50 each at par. Let \( Y \) be the number of 4% shares purchased. The total investment can be expressed as:
\[ Y \times 50 = 9500 \]

Now, solving for \( Y \):
\[ Y = \frac{9500}{50} = 190 \]

### Step 5: Calculate the final income from the 4% shares
The income from the 4% shares is calculated as:
\[ \text{Final income} = Y \times \text{Dividend rate} = 190 \times 4 = 760 \]

### Step 6: Calculate the change in income
To find the change in income, we subtract the initial income from the final income:
\[ \text{Change in income} = \text{Final income} - \text{Initial income} = 760 - 300 = 460 \]

### Final Result
The change in his income is Rs 460.

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