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The problem from the image reads as follows:

**Question**: A trader earns 20% profit by selling an article. If he increases the selling price by 50%, his gain percentage increases to 57%. What was the selling price of the article if he sells it at 20% profit?
   
Options:
a) 1350  
b) 1380  
c) 1450  
d) 1560

---

### Solution:

Let the **cost price (C.P.)** of the article be \( x \).

- When the trader earns a 20% profit, the **selling price (S.P.)** is:
  \[
  S.P_1 = C.P. + 20\% \text{ of C.P.} = C.P. + 0.2 \cdot C.P. = 1.2 \cdot C.P.
  \]
  So, the selling price at 20% profit is \( 1.2x \).

- When the trader increases the selling price by 50%, the new selling price becomes:
  \[
  S.P_2 = 1.5 \cdot S.P_1 = 1.5 \cdot 1.2x = 1.8x.
  \]
  
- According to the question, at this new selling price, the trader's profit percentage increases to 57%. So, the profit on selling at \( S.P_2 \) is 57%. This implies:
  \[
  S.P_2 = C.P. + 57\% \text{ of C.P.} = C.P. + 0.57 \cdot C.P. = 1.57 \cdot C.P.
  \]

Now, equate the two expressions for \( S.P_2 \):
\[
1.8x = 1.57x
\]

- Solving for \( x \), we get:
  \[
  x = \frac{1.8}{1.57} \cdot S.P_1
  \]



A trader earns 20% profit by selling an article. If he increases the selling price by 50%, his gain percentage increases to 57%. What was the selling price of the article if he sells it at 20% profit?
Options:
a) 1350
b) 1380
c) 1450
d) 1560

Learn how to solve a profit and selling price problem where a trader earns 20% profit, increases the selling price by 50%, and the profit increases to 57%. The step-by-step solution involves calculating the cost price and selling price using percentage formulas. Suitable for students in Grades 9-10.

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