Read the following information carefully and answer given question below:
Abhishek bought some chairs and tables from a shopkeeper. The prices of a chair and table were in the ratio of 5:8. The shopkeeper have discounts of `20%` and `25%` on the chair and the table respectively. The ratio of number of chairs and tables bought by Abhishek is 6:5.
If Abhishek sells each chair and table bought by him at discount of `25%` and `20%` respectively after marking up the price of both by `50%` and gives one table free for every four chair bought by a customer and only `2/3` rd of the total chair are sold in bunch of four chair, then what is the net profit/loss made by Abhishek after selling all of the items which he bought from the shopkeeper?

Options

A. `6 2/3%`
B. `3 1/3%`
C. `2 9/9%`
D. `4 1/4%`

Answer

To solve the problem step by step, let's break it down into manageable parts.

### Step 1: Determine the Cost Price of Chairs and Tables
Let the cost price of a chair be \(5x\) and the cost price of a table be \(8x\).

### Step 2: Calculate the Discounts
- Discount on chairs = 20% of \(5x\) = \(0.2 \times 5x = x\)
- Selling price of a chair after discount = \(5x - x = 4x\)

- Discount on tables = 25% of \(8x\) = \(0.25 \times 8x = 2x\)
- Selling price of a table after discount = \(8x - 2x = 6x\)

### Step 3: Determine the Number of Chairs and Tables Bought
The ratio of the number of chairs to tables is 6:5. Let the number of chairs be \(6y\) and the number of tables be \(5y\).

### Step 4: Calculate the Total Cost Price
Total cost price of chairs = \(6y \times 5x = 30xy\)

Total cost price of tables = \(5y \times 8x = 40xy\)

Total cost price = \(30xy + 40xy = 70xy\)

### Step 5: Calculate the Total Selling Price
- Total selling price of chairs = \(6y \times 4x = 24xy\)
- Total selling price of tables = \(5y \times 6x = 30xy\)

Total selling price = \(24xy + 30xy = 54xy\)

### Step 6: Calculate the Number of Chairs Sold
Only \( \frac{2}{3} \) of the total chairs are sold in bunches of 4.
Total chairs = \(6y\)
Chairs sold = \( \frac{2}{3} \times 6y = 4y\)

### Step 7: Calculate the Number of Tables Given Free
For every 4 chairs sold, 1 table is given free.
Total tables given free = \( \frac{4y}{4} = y\)

### Step 8: Calculate the Effective Selling Price of Tables
Since \(y\) tables are given free, the effective selling price of tables sold = \(5y - y = 4y\)

### Step 9: Calculate the Total Selling Price Considering Free Tables
Total selling price considering free tables = \(24xy + 30xy - 6xy = 48xy\)

### Step 10: Calculate Profit or Loss
Profit/Loss = Total Selling Price - Total Cost Price
Profit/Loss = \(48xy - 70xy = -22xy\)

### Step 11: Calculate the Net Profit/Loss Percentage
Net Profit/Loss Percentage = \(\frac{\text{Profit/Loss}}{\text{Total Cost Price}} \times 100\)
Net Profit/Loss Percentage = \(\frac{-22xy}{70xy} \times 100 = -31.43\%\)

### Final Answer
Abhishek incurs a loss of approximately 31.43%.

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