On selling 70 articles for Rs 160 a person incurred loss of 20%. How many articles he should sell for Rs 96 to earn profit of 20%.

Answer

To solve the problem step by step, we will first determine the cost price of the articles and then calculate how many articles need to be sold to earn a profit of 20%.

### Step 1: Calculate the Cost Price (CP) of One Article
We know that selling 70 articles incurs a loss of 20%.

Let the Cost Price (CP) of one article be \( x \).

The Selling Price (SP) for 70 articles is given as Rs. 160.

Using the formula for loss:
\[ \text{Loss} = \text{CP} - \text{SP} \]
Since there is a loss of 20%, we can express this as:
\[ \text{SP} = \text{CP} - 0.2 \times \text{CP} = 0.8 \times \text{CP} \]
Thus, we have:
\[ 160 = 0.8 \times (70 \times x) \]
\[ 160 = 56x \]
Now, solving for \( x \):
\[ x = \frac{160}{56} = \frac{20}{7} \text{ Rs.} \]

### Step 2: Calculate the Selling Price for 20% Profit
To earn a profit of 20%, the Selling Price (SP) must be:
\[ \text{SP} = \text{CP} + 0.2 \times \text{CP} = 1.2 \times \text{CP} \]
Substituting the value of CP:
\[ \text{SP} = 1.2 \times \left(\frac{20}{7}\right) = \frac{24}{7} \text{ Rs. per article} \]

### Step 3: Determine the Number of Articles to Sell for Rs. 96
We need to find how many articles (let's call this \( n \)) can be sold for Rs. 96 at the new SP:
\[ n \times \frac{24}{7} = 96 \]
Now, solving for \( n \):
\[ n = \frac{96 \times 7}{24} = \frac{672}{24} = 28 \]

### Conclusion
The person should sell **28 articles** for Rs. 96 to earn a profit of 20%.

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