A man would gain 20% by selling a chair for Rs. 47.5 and would gain 15% by selling a table for Rs. 57.5. He sells the chair for Rs. 36, what is the least price for which he must sell the table to avoid any loss on the two together

Options

A. Rs. 50.2
B. Rs. 55.8
C. Rs. 60
D. Rs. 53.6

Answer

To solve the problem step by step, we will first determine the cost price of the chair and the table based on the given selling prices and profit percentages. Then, we will calculate the selling price of the table needed to avoid any loss when the chair is sold at a lower price.

### Step 1: Calculate the Cost Price of the Chair
The selling price of the chair is Rs. 47.5, and the profit percentage is 20%.

Let the cost price of the chair be \( CP_{chair} \).

Using the formula for selling price (SP) in terms of cost price (CP) and profit percentage (P%):
\[ SP = CP + (P\% \times CP) \]
This can be rearranged to:
\[ SP = CP \times \left(1 + \frac{P\%}{100}\right) \]

Substituting the values:
\[ 47.5 = CP_{chair} \times \left(1 + \frac{20}{100}\right) \]
\[ 47.5 = CP_{chair} \times 1.2 \]

Now, solving for \( CP_{chair} \):
\[ CP_{chair} = \frac{47.5}{1.2} = 39.5833 \text{ (approximately Rs. 39.58)} \]

### Step 2: Calculate the Cost Price of the Table
The selling price of the table is Rs. 57.5, and the profit percentage is 15%.

Let the cost price of the table be \( CP_{table} \).

Using the same formula:
\[ 57.5 = CP_{table} \times \left(1 + \frac{15}{100}\right) \]
\[ 57.5 = CP_{table} \times 1.15 \]

Now, solving for \( CP_{table} \):
\[ CP_{table} = \frac{57.5}{1.15} = 50 \]

### Step 3: Determine the Loss from Selling the Chair
The chair is sold for Rs. 36. We need to find out the loss incurred from this transaction:
\[ \text{Loss from chair} = CP_{chair} - \text{Selling Price of chair} \]
\[ \text{Loss from chair} = 39.5833 - 36 = 3.5833 \text{ (approximately Rs. 3.58)} \]

### Step 4: Calculate the Selling Price of the Table to Avoid Overall Loss
To avoid any loss on the two transactions together, the total loss from the chair must be compensated by the profit from the table.

The cost price of the table is Rs. 50. Therefore, the selling price of the table must be:
\[ \text{Required Selling Price of table} = CP_{table} + \text{Loss from chair} \]
\[ \text{Required Selling Price of table} = 50 + 3.5833 = 53.5833 \text{ (approximately Rs. 53.58)} \]

### Step 5: Round Off the Selling Price
To find the least price, we round Rs. 53.5833 to Rs. 53.6.

### Final Answer
The least price for which he must sell the table to avoid any loss on the two together is **Rs. 53.6**.

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