If 6 articles are sold for Rs 1 then there is a loss of 20%. In order to gain 20%, what must be the number of articles sold for Rs 1 ?

Answer

To solve the problem step by step, we need to determine the cost price of one article and then find out how many articles need to be sold at a certain price to achieve a gain of 20%.

### Step 1: Determine the Selling Price of One Article
Given that 6 articles are sold for Rs. 1, we can find the selling price (SP) of one article.

\[ \text{Selling Price of 1 article} = \frac{1}{6} \text{ Rs} \]

### Step 2: Calculate the Cost Price Using the Loss Percentage
We know that there is a loss of 20%. This means that the selling price is 80% of the cost price (CP). We can express this relationship mathematically:

\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]

Substituting the values we have:

\[ \frac{1}{6} = \text{CP} \times \left(1 - \frac{20}{100}\right) \]

This simplifies to:

\[ \frac{1}{6} = \text{CP} \times 0.8 \]

### Step 3: Solve for the Cost Price
Now, we can solve for the cost price (CP):

\[ \text{CP} = \frac{1}{6} \div 0.8 = \frac{1}{6} \times \frac{10}{8} = \frac{10}{48} = \frac{5}{24} \text{ Rs} \]

### Step 4: Calculate the Selling Price for a Gain of 20%
To find the selling price for a gain of 20%, we use the formula:

\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Gain \%}}{100}\right) \]

Substituting the values:

\[ \text{SP} = \frac{5}{24} \times \left(1 + \frac{20}{100}\right) \]

This simplifies to:

\[ \text{SP} = \frac{5}{24} \times 1.2 = \frac{5 \times 12}{24 \times 10} = \frac{5}{20} = \frac{1}{4} \text{ Rs} \]

### Step 5: Determine the Number of Articles Sold for Rs. 1
Now, we need to find out how many articles can be sold for Rs. 1 at this new selling price of Rs. 1/4.

\[ \text{Number of articles sold for Rs. 1} = \frac{1}{\text{SP of 1 article}} = \frac{1}{\frac{1}{4}} = 4 \]

### Final Answer
Thus, to gain 20%, **4 articles must be sold for Rs. 1**.

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