A loss of 20% is incurred when 6 articles are sold for a rupee.To gain 20% how many articles should be sold for a rupee ?

Options

A. a) 1
B. b) 2
C. c) 3
D. d) 4

Answer

To solve the problem step by step, we need to determine how many articles should be sold for a rupee to gain a profit of 20%, given that a loss of 20% occurs when 6 articles are sold for a rupee.

### Step 1: Determine the Cost Price (CP) of One Article
When 6 articles are sold for Rs. 1, and there is a loss of 20%, we can first find the Cost Price (CP) of one article.

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

Since a loss of 20% means that the Selling Price (SP) is 80% of the Cost Price, we can write the equation:

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

Given that \( SP = 1 \) (for 6 articles), we have:

\[ 1 = CP \times 0.8 \]

Now, solving for \( CP \):

\[ CP = \frac{1}{0.8} = 1.25 \]

So, the Cost Price of one article is Rs. 1.25.

### Step 2: Determine the Selling Price (SP) for a 20% Profit
To find out how many articles we need to sell for a rupee to achieve a profit of 20%, we first need to calculate the new Selling Price (SP) for a 20% profit.

The Selling Price with a 20% profit can be calculated as:

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

Substituting the values we have:

\[ SP = 1.25 \times \left(1 + \frac{20}{100}\right) = 1.25 \times 1.2 = 1.5 \]

So, the Selling Price for a 20% profit is Rs. 1.5.

### Step 3: Calculate the Number of Articles to Sell 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. 1.5.

Let \( n \) be the number of articles sold for Rs. 1. The equation can be set up as:

\[ n \times SP = 1 \]

Substituting the SP we found:

\[ n \times 1.5 = 1 \]

Now, solving for \( n \):

\[ n = \frac{1}{1.5} = \frac{2}{3} \]

### Step 4: Convert to Articles Sold for Rs. 1
Since we want to know how many articles can be sold for Rs. 1, we can also express this in terms of how many articles can be sold for Rs. 1:

If the SP is Rs. 1.5 for one article, then for Rs. 1, we can sell:

\[ \text{Number of articles} = \frac{1}{\frac{1.5}{1}} = \frac{2}{3} \]

This means that to gain a profit of 20%, we can sell \( \frac{2}{3} \) of an article for Rs. 1.

### Final Answer
To gain a profit of 20%, you should sell 4 articles for Rs. 1.