A shopkeeper sells two power banks for 960 each. On one he gains 20% and on the other he incurs a loss of 20%. What was his gain or loss in the overall transaction?
(a)4% gains
(b)5% loss
(c)4% loss
(d)5% gain

Options

A. 4% gains
B. 5% loss
C. 4% loss
D. 5% gain

Answer

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

### Step 1: Understand the Selling Price (SP) and Profit/Loss
The shopkeeper sells two power banks for ₹960 each. Therefore, the selling price (SP) for each power bank is:
- SP of Power Bank 1 = ₹960
- SP of Power Bank 2 = ₹960

### Step 2: Calculate the Cost Price (CP) for Each Power Bank
1. **Power Bank 1**:
- He gains 20% on this power bank.
- Let the cost price (CP) of Power Bank 1 be \( CP_1 \).
- Since the gain is 20%, we can express this as:
\[ SP = CP + 20\% \text{ of } CP \implies 960 = CP_1 + 0.2 \times CP_1 \]
- This simplifies to:
\[ 960 = 1.2 \times CP_1 \implies CP_1 = \frac{960}{1.2} = 800 \]

2. **Power Bank 2**:
- He incurs a loss of 20% on this power bank.
- Let the cost price (CP) of Power Bank 2 be \( CP_2 \).
- Since the loss is 20%, we can express this as:
\[ SP = CP - 20\% \text{ of } CP \implies 960 = CP_2 - 0.2 \times CP_2 \]
- This simplifies to:
\[ 960 = 0.8 \times CP_2 \implies CP_2 = \frac{960}{0.8} = 1200 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
- Total Cost Price (CP) = \( CP_1 + CP_2 = 800 + 1200 = 2000 \)
- Total Selling Price (SP) = \( SP_1 + SP_2 = 960 + 960 = 1920 \)

### Step 4: Calculate Overall Gain or Loss
- Overall Loss = Total CP - Total SP
- Overall Loss = \( 2000 - 1920 = 80 \)

### Step 5: Calculate the Percentage Loss
- Percentage Loss = \( \frac{\text{Loss}}{\text{Total CP}} \times 100 \)
- Percentage Loss = \( \frac{80}{2000} \times 100 = 4\% \)

### Conclusion
The shopkeeper incurs a **4% loss** in the overall transaction.

### Answer
(c) 4% loss

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