A dealer buys 50 chairs for Rs 50,000 but 20 of them are damaged. He decides to sell each damaged one at three fourths the price of the normal one. What should this price be in order that he may make a profit of 35% on the whole transaction?

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Cost Price of One Chair
The dealer buys 50 chairs for Rs 50,000.

**Cost Price of 50 chairs = Rs 50,000**
**Cost Price of 1 chair = Total Cost Price / Number of Chairs**
Cost Price of 1 chair = Rs 50,000 / 50 = Rs 1,000

### Step 2: Calculate Selling Price of Damaged Chairs
20 chairs are damaged, and the dealer decides to sell each damaged chair at three-fourths the price of a normal chair.

**Selling Price of 1 damaged chair = (3/4) * Cost Price of 1 chair**
Selling Price of 1 damaged chair = (3/4) * Rs 1,000 = Rs 750

Now, calculate the total selling price for the 20 damaged chairs:

**Total Selling Price of 20 damaged chairs = 20 * Selling Price of 1 damaged chair**
Total Selling Price of 20 damaged chairs = 20 * Rs 750 = Rs 15,000

### Step 3: Calculate Required Selling Price for Profit
The dealer wants to make a profit of 35% on the whole transaction.

**Profit Percentage = 35%**
**Total Cost Price = Rs 50,000**
**Required Selling Price (SP) for 35% profit = Cost Price + Profit**
Profit = (Profit Percentage / 100) * Cost Price
Profit = (35 / 100) * Rs 50,000 = Rs 17,500

Now, calculate the total required selling price:

**Required Selling Price = Cost Price + Profit**
Required Selling Price = Rs 50,000 + Rs 17,500 = Rs 67,500

### Step 4: Calculate Selling Price of Undamaged Chairs
We know the total selling price of the 20 damaged chairs is Rs 15,000.

**Total Selling Price of 50 chairs = Rs 67,500**
**Selling Price of 30 undamaged chairs = Total Selling Price - Selling Price of 20 damaged chairs**
Selling Price of 30 undamaged chairs = Rs 67,500 - Rs 15,000 = Rs 52,500

### Step 5: Calculate Selling Price of One Undamaged Chair
Now, we need to find the selling price of one undamaged chair.

**Selling Price of 1 undamaged chair = Total Selling Price of 30 undamaged chairs / Number of undamaged chairs**
Selling Price of 1 undamaged chair = Rs 52,500 / 30 = Rs 1,750

### Final Answer
The price at which the dealer should sell each undamaged chair to make a profit of 35% is **Rs 1,750**.

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