Let's analyze the problem step-by-step:
Given:
- The shopkeeper expects a gain of 2 on his cost price.
- Total sales in a week = Rs. 392.
- We need to find the profit.
Step 1: Understand the gain
The gain is 2 on the cost price, which means the gain percentage is 2%. This implies:
Gain=2% of Cost Price (CP)\text{Gain}=2%\text{ of Cost Price (CP)}Gain=2% of Cost Price (CP)
Step 2: Express Selling Price (SP)
Selling Price is the Cost Price plus the gain:
SP=CP+Gain=CP+2%×CP=CP×(1+2100)=1.02×CPSP=CP+\text{Gain}=CP+2%\times CP=CP\times (1+\frac{2}{100})=1.02\times CPSP=CP+Gain=CP+2%×CP=CP×(1+1002)=1.02×CP
Step 3: Use the total sales to find Cost Price
Total sales (SP) = Rs. 392
392=1.02×CP392=1.02\times CP392=1.02×CP
CP=3921.02=384.31 (approx)CP=\frac{392}{1.02}=384.31\text{ (approx)}CP=1.02392=384.31 (approx)
Step 4: Calculate the profit
Profit = Selling Price - Cost Price
Profit=392−384.31=7.69 Rs. (approx)\text{Profit}=392-384.31=7.69\text{ Rs. (approx)}Profit=392−384.31=7.69 Rs. (approx)
Final answer:
The shopkeeper's profit was approximately Rs. 7.69.
