Three items are purchased at Rs 4500 each. One of them is sold at a loss of 10%. At what price should the other two be sold so as to gain 20% on the whole transaction? What is the gain % on these two items?

Answer

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

### Step 1: Determine the Cost Price of Each Item
Each item is purchased at Rs 4500.

- Cost Price (CP) of each item = Rs 4500

### Step 2: Calculate the Selling Price of the First Item
The first item is sold at a loss of 10%.

- Loss = 10% of CP
- Selling Price (SP1) = CP1 - Loss
- SP1 = 4500 - (10/100) * 4500
- SP1 = 4500 - 450 = Rs 4050

### Step 3: Calculate the Total Cost Price of All Items
The total cost price (CP) for three items:

- Total CP = CP1 + CP2 + CP3
- Total CP = 4500 + 4500 + 4500 = Rs 13500

### Step 4: Calculate the Desired Selling Price for a 20% Gain
To achieve a 20% gain on the total transaction:

- Desired Selling Price (SP) = Total CP + 20% of Total CP
- SP = 13500 + (20/100) * 13500
- SP = 13500 + 2700 = Rs 16200

### Step 5: Calculate the Selling Price of the Other Two Items
Let the selling prices of the second and third items be SP2 and SP3.

- SP2 + SP3 = Total SP - SP1
- SP2 + SP3 = 16200 - 4050
- SP2 + SP3 = Rs 12150

### Step 6: Calculate the Cost Price of the Other Two Items
The cost price of the second and third items:

- CP2 + CP3 = 4500 + 4500 = Rs 9000

### Step 7: Calculate the Gain on the Second and Third Items
Gain on the second and third items:

- Gain = (SP2 + SP3) - (CP2 + CP3)
- Gain = 12150 - 9000
- Gain = Rs 3150

### Step 8: Calculate the Gain Percentage on the Second and Third Items
Gain percentage is calculated as follows:

- Gain Percentage = (Gain / (CP2 + CP3)) * 100
- Gain Percentage = (3150 / 9000) * 100
- Gain Percentage = 0.35 * 100 = 35%

### Final Answers:
1. The selling price of the other two items combined should be Rs 12150.
2. The gain percentage on these two items is 35%.

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