A man sold two articles at the same S.P First article was sold at 18.75% prfit. Af what loss % he would have sold second article, So that neither profit nor loss?

Let's solve the problem step by step.

### Given:
- The man sold two articles at the same selling price (S.P).
- The first article was sold at an 18.75% profit.
- The second article is to be sold at a loss such that there is neither profit nor loss overall.

### Let's denote:
- \( C_1 \) = Cost price of the first article.
- \( C_2 \) = Cost price of the second article.
- \( S.P \) = Selling price of each article.

### Step 1: Express the Selling Price of the First Article
Since the first article was sold at an 18.75% profit:
\[
S.P = C_1 \times \left(1 + \frac{18.75}{100}\right) = C_1 \times \frac{118.75}{100} = C_1 \times \frac{475}{400}
\]

### Step 2: Express the Selling Price of the Second Article
Let the loss percentage on the second article be \( x \% \). Then, the selling price of the second article would be:
\[
S.P = C_2 \times \left(1 - \frac{x}{100}\right)
\]

### Step 3: Set the Selling Prices Equal
Since the selling prices are the same:
\[
C_1 \times \frac{475}{400} = C_2 \times \left(1 - \frac{x}{100}\right)
\]

### Step 4: Condition of No Profit, No Loss
For there to be no profit or loss overall, the total cost price must equal the total selling price:
\[
C_1 + C_2 = S.P + S.P = 2 \times S.P
\]

Substituting the expressions for \( S.P \):
\[
C_1 + C_2 = 2 \times S.P
\]

### Step 5: Simplify and Solve for \( x \)
Substitute \( S.P = C_1 \times \frac{475}{400} \) into the equation:

\[
C_1 + C_2 = 2 \times \left(C_1 \times \frac{475}{400}\right)
\]

We now have two equations:

1. \( C_1 + C_2 = 2 \times S.P \)
2. \( S.P = C_1 \times \frac{475}{400} = C_2 \times \left(1 - \frac{x}{100}\right) \)

Using these equations and solving for \( x \), you will find the loss percentage on the second article. Let's simplify further to find \( x \).

### Solving for \( x \):
From the first equation:
\[
S.P = C_1 \times \frac{475}{400} = C_2 \times \left(1 - \frac{x}{100}\right)
\]

So,
\[
C_1 \times \frac{475}{400} = C_2 \times \left(1 - \frac{x}{100}\right)
\]

Now, since \( C_1 + C_2 = 2 \times C_1 \times \frac{475}{400} \):
\[
\frac{C_1 \times 475}{400} + C_2 = \frac{C_1 \times 950}{400}
\]

So, \( C_2 = \frac{C_1 \times 475}{400} \).

Substitute into the original equation to find \( x \):

\[
\frac{C_1 \times 475}{400} = C_2 \times \left(1 - \frac{x}{100}\right)
\]

Since \( C_2 = \frac{C_1 \times 475}{400} \):

\[
\frac{C_1 \times 475}{400} = \frac{C_1 \times 475}{400} \times \left(1 - \frac{x}{100}\right)
\]

Thus, \( x = 18.75\% \).

### Final Answer:
The loss percentage on the second article should be **18.75%** to have neither profit nor loss overall.

Do you have any questions, or would you like further details on any part of the solution?

---

1. What happens if the loss percentage is higher than the profit percentage?
2. How does the concept of selling price affect the overall profit or loss?
3. Can this problem be generalized for any profit and loss percentage?
4. How would the solution change if the articles were sold at different selling prices?
5. What if the profit was lower than the loss percentage?

**Tip:** Always keep track of each variable when dealing with multiple items to avoid confusion.

Explore how to solve a profit and loss problem where a man sells two articles at the same selling price, with the first article sold at an 18.75% profit. Learn the step-by-step solution to find the loss percentage needed on the second article to achieve neither profit nor loss overall.

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