Rohit invested `9600rs` on `100rs` shares at `20rs` premium paying `8%` dividend. Rohit sold the shares when the price rose to `160rs` . He invested the proceeds (excluding dividend) in `10%` `50rs` shares at `40rs` find the
(i) original number of shares
(ii) sale proceeds
(iii) new number of shares
(iv) change in the two dividends

Answer

Let's solve the problem step by step.

### Given:
- Total investment = ₹9600
- Face value of shares = ₹100
- Premium on shares = ₹20
- Dividend rate = 8%
- Selling price of shares = ₹160
- New investment in shares = 10% of ₹50 shares at ₹40

### (i) Original Number of Shares

1. **Calculate the market value of the shares:**
\[ \text{Market Value} = \text{Face Value} + \text{Premium} = 100 + 20 = ₹120 \]

2. **Calculate the number of shares:**
\[ \text{Number of Shares} = \frac{\text{Total Investment}}{\text{Market Value}} = \frac{9600}{120} = 80 \]

### (ii) Sale Proceeds

1. **Calculate the sale proceeds:**
\[ \text{Sale Proceeds} = \text{Number of Shares} \times \text{Selling Price} = 80 \times 160 = ₹12800 \]

### (iii) New Number of Shares

1. **Calculate the new number of shares purchased:**
- Proceeds from sale (excluding dividend) = ₹12800
- Market value of new shares = ₹40
\[ \text{New Number of Shares} = \frac{\text{Proceeds}}{\text{Market Value of New Shares}} = \frac{12800}{40} = 320 \]

### (iv) Change in the Two Dividends

1. **Calculate the dividend from the original investment:**
- Dividend per share = 8% of ₹100 = ₹8
\[ \text{Total Dividend from Original Investment} = \text{Number of Shares} \times \text{Dividend per Share} = 80 \times 8 = ₹640 \]

2. **Calculate the dividend from the new investment:**
- Dividend per share = 10% of ₹50 = ₹5
\[ \text{Total Dividend from New Investment} = \text{New Number of Shares} \times \text{Dividend per Share} = 320 \times 5 = ₹1600 \]

3. **Calculate the change in dividends:**
\[ \text{Change in Dividends} = \text{Total Dividend from New Investment} - \text{Total Dividend from Original Investment} = 1600 - 640 = ₹960 \]

### Summary of Results:
- (i) Original Number of Shares = 80
- (ii) Sale Proceeds = ₹12800
- (iii) New Number of Shares = 320
- (iv) Change in the Two Dividends = ₹960