By selling 20 articles for a rupee a man loses 10%. How many for a rupee did he buy ?

Options

A. 16
B. 18
C. 14
D. none of these

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the Selling Price and Loss
We know that the man sells 20 articles for 1 rupee. This means:
- Selling Price (SP) of 20 articles = 1 rupee

### Step 2: Calculate the Selling Price of One Article
To find the selling price of one article, we divide the total selling price by the number of articles:
- Selling Price of 1 article = 1 rupee / 20 articles = 1/20 rupee

### Step 3: Determine the Loss Percentage
The problem states that the man incurs a loss of 10%. This means:
- Cost Price (CP) is 100%
- Selling Price (SP) is 90% of the Cost Price (CP)

### Step 4: Relate Selling Price and Cost Price
Since we know that the Selling Price (SP) is 90% of the Cost Price (CP), we can express this relationship mathematically:
- SP = 90% of CP
- SP = (90/100) * CP

### Step 5: Substitute the Selling Price
Now, we substitute the Selling Price of one article into the equation:
- 1/20 = (90/100) * CP
- To find CP, we rearrange the equation:
- CP = (1/20) * (100/90)

### Step 6: Simplify to Find Cost Price
Now, let's simplify:
- CP = (1/20) * (10/9) = 10/180 = 1/18 rupee

### Step 7: Calculate How Many Articles Can Be Bought for 1 Rupee
If the Cost Price of one article is 1/18 rupee, then to find out how many articles can be bought for 1 rupee, we take the reciprocal:
- Number of articles for 1 rupee = 1 / (1/18) = 18 articles

### Conclusion
Thus, the man bought 18 articles for 1 rupee.

### Final Answer
The answer is: **18 articles.**

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