Mrs. Kulkarni invests `131040rs` in buying `100rs` shares at a discount of `9%`. She sells shares worth `72000` at a premium of `10%` and the rest at a discount of `5%`. Find her total gain or loss on the whole.

Answer

To solve the problem step by step, we will follow the calculations as described in the video transcript.

### Step 1: Determine the Market Value of One Share
The market value of one share is calculated by applying the discount of 9% on the estimated value of the share, which is ₹100.

\[ \text{Market Value} = \text{Estimated Value} - \text{Discount} \]
\[ \text{Discount} = 9\% \text{ of } 100 = \frac{9}{100} \times 100 = 9 \]
\[ \text{Market Value} = 100 - 9 = 91 \text{ rupees} \]

### Step 2: Calculate the Number of Shares Purchased
Mrs. Kulkarni invested ₹131040 in shares, and the market value of each share is ₹91. The number of shares purchased can be calculated as follows:

\[ \text{Number of Shares} = \frac{\text{Total Investment}}{\text{Market Value}} \]
\[ \text{Number of Shares} = \frac{131040}{91} = 1440 \text{ shares} \]

### Step 3: Calculate the Selling Price of Shares Sold at a Premium
Mrs. Kulkarni sells shares worth ₹72000 at a premium of 10%. First, we need to find the market value of one share when sold at a premium:

\[ \text{Market Value at Premium} = \text{Estimated Value} + \text{Premium} \]
\[ \text{Premium} = 10\% \text{ of } 100 = \frac{10}{100} \times 100 = 10 \]
\[ \text{Market Value at Premium} = 100 + 10 = 110 \text{ rupees} \]

Next, we calculate the number of shares sold at this price:

\[ \text{Number of Shares Sold at Premium} = \frac{72000}{110} = 720 \text{ shares} \]

### Step 4: Calculate the Selling Price of Remaining Shares Sold at a Discount
The remaining shares are:

\[ \text{Remaining Shares} = \text{Total Shares} - \text{Shares Sold at Premium} \]
\[ \text{Remaining Shares} = 1440 - 720 = 720 \text{ shares} \]

Now, we calculate the market value of one share when sold at a discount of 5%:

\[ \text{Market Value at Discount} = \text{Estimated Value} - \text{Discount} \]
\[ \text{Discount} = 5\% \text{ of } 100 = \frac{5}{100} \times 100 = 5 \]
\[ \text{Market Value at Discount} = 100 - 5 = 95 \text{ rupees} \]

Now, we can find the selling price of the remaining shares:

\[ \text{Selling Price of Remaining Shares} = \text{Remaining Shares} \times \text{Market Value at Discount} \]
\[ \text{Selling Price of Remaining Shares} = 720 \times 95 = 68400 \text{ rupees} \]

### Step 5: Calculate Total Selling Price
Now we can find the total selling price from both transactions:

\[ \text{Total Selling Price} = \text{Selling Price at Premium} + \text{Selling Price at Discount} \]
\[ \text{Total Selling Price} = 72000 + 68400 = 140400 \text{ rupees} \]

### Step 6: Calculate Gain or Loss
Finally, we calculate the gain or loss by comparing the total selling price with the total investment:

\[ \text{Gain or Loss} = \text{Total Selling Price} - \text{Total Investment} \]
\[ \text{Gain or Loss} = 140400 - 131040 = 9360 \text{ rupees} \]

Since the total selling price is greater than the total investment, Mrs. Kulkarni has made a gain of ₹9360.

### Final Answer
Mrs. Kulkarni's total gain is ₹9360.

---