Question-1: By selling a books for Tk.675, a seller losses 7/9 of his outlay. By selling it for Tk.810, his gain or loses percentange is?

Let's break down the problem step by step.

### Step 1: Define the variables
Let the cost price of the book be \( x \). According to the problem:
- When the book is sold for Tk.675, the seller incurs a loss of \( \frac{7}{9} \) of his outlay (cost price).

Thus, we can express this as:
\[
\text{Loss} = \frac{7}{9} \times x
\]
Since loss is the difference between cost price and selling price, we have:
\[
x - 675 = \frac{7}{9} \times x
\]

### Step 2: Solve for \( x \)
Rearrange the equation:
\[
x - \frac{7}{9}x = 675
\]
\[
\frac{2}{9}x = 675
\]
Now solve for \( x \):
\[
x = \frac{675 \times 9}{2}
\]
\[
x = 3037.5
\]
So, the cost price \( x \) is Tk.3037.5.

### Step 3: Determine the percentage gain or loss when sold at Tk.810
Now, the book is sold at Tk.810. To find the gain or loss, we compare the selling price (Tk.810) with the cost price (Tk.3037.5).

#### Loss Calculation
\[
\text{Loss} = 3037.5 - 810 = 2227.5
\]
The loss percentage is:
\[
\text{Loss percentage} = \frac{2227.5}{3037.5} \times 100
\]
\[
\text{Loss percentage} \approx 73.33\%
\]

### Final Answer:
The seller incurs a loss of approximately **73.33%** when selling the book for Tk.810.

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Would you like further clarification or additional details?

Here are some related questions to explore:
1. How do you calculate gain or loss percentage based on selling and cost price?
2. What is the formula to calculate the selling price when a percentage gain is known?
3. How can you calculate the selling price to break even?
4. What is the effect of changing the selling price on gain or loss percentage?
5. How does the loss percentage change if the cost price is increased?

**Tip:** Always express cost price, selling price, and loss/gain percentages in the same units to avoid confusion during calculations.

By selling a book for Tk.675, a seller loses 7/9 of his outlay. By selling it for Tk.810, what is his gain or loss percentage?

Learn how to calculate the loss percentage when a book is sold for Tk.810, given the cost price and loss from the previous sale. This step-by-step solution covers profit and loss concepts and percentage calculations, suitable for students in Grades 8-10.

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