A shopkeeper purchases two Items for Rs. 520. One of them is sold gaining 16% and the other at a loss of 10%, thus making no profit or loss. What is the selling price of the item sold at loss?

Options

A. Rs.288
B. Rs.232
C. Rs.320
D. Rs.200

Answer

To solve the problem step by step, we will use the information provided in the question regarding the purchase, profit, and loss of the items.

### Step 1: Understand the total cost price
The shopkeeper purchases two items for Rs. 520. Let's denote the cost price of the first item as CP1 and the cost price of the second item as CP2.

**Equation:**
CP1 + CP2 = 520

### Step 2: Define the profit and loss
The first item is sold at a gain of 16%, and the second item is sold at a loss of 10%. Since the overall transaction results in no profit or loss, we can set up the following equations for the selling prices:

- Selling Price of Item 1 (SP1) = CP1 + 16% of CP1 = CP1 + 0.16 * CP1 = 1.16 * CP1
- Selling Price of Item 2 (SP2) = CP2 - 10% of CP2 = CP2 - 0.10 * CP2 = 0.90 * CP2

### Step 3: Set up the equation for no profit or loss
According to the problem, the total selling price of both items equals the total cost price:

**Equation:**
SP1 + SP2 = CP1 + CP2
1.16 * CP1 + 0.90 * CP2 = 520

### Step 4: Substitute CP2 from the first equation
From the first equation, we can express CP2 in terms of CP1:
CP2 = 520 - CP1

### Step 5: Substitute CP2 in the selling price equation
Now substitute CP2 in the selling price equation:
1.16 * CP1 + 0.90 * (520 - CP1) = 520

### Step 6: Simplify the equation
Now, simplify the equation:
1.16 * CP1 + 468 - 0.90 * CP1 = 520

Combine like terms:
(1.16 - 0.90) * CP1 + 468 = 520
0.26 * CP1 + 468 = 520

### Step 7: Solve for CP1
Now, isolate CP1:
0.26 * CP1 = 520 - 468
0.26 * CP1 = 52
CP1 = 52 / 0.26
CP1 = 200

### Step 8: Find CP2
Now, substitute CP1 back to find CP2:
CP2 = 520 - CP1
CP2 = 520 - 200
CP2 = 320

### Step 9: Calculate the selling price of the item sold at loss
The second item is sold at a loss of 10%. Therefore, the selling price of the second item (SP2) is:
SP2 = CP2 - 10% of CP2
SP2 = 320 - 0.10 * 320
SP2 = 320 - 32
SP2 = 288

### Final Answer
The selling price of the item sold at a loss is Rs. 288.

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