Cost price of 20 articles is equal to selling price of x articles. If the profit is 25%, then the value of x is:

Q: Cost price of 20 articles is equal to selling price of x articles. If the profit is 25%, then the value of x is:

To determine the value of $ x $ where the cost price of 20 articles is equal to the selling price of $ x $ articles with a profit of 25%, we need to follow these steps: 1. **Understanding the Profit Percentage:** - A profit of 25% means that the selling price (SP) is 125% of the cost price (CP). 2. **Setting Up the Equation:** - Let the cost price of one article be $ CP $. - Therefore, the cost price of 20 articles is $ 20 \times CP $. - The selling price of one article, considering a 25% profit, is $ 1.25 \times CP $. 3. **Relating Cost Price and Selling Price:** - According to the problem, the cost price of 20 articles is equal to the selling price of $ x $ articles. - Therefore, $ 20 \times CP = x \times 1.25 \times CP $. 4. **Solving for $ x $:** - Simplify the equation: $ 20 = x \times 1.25 $. - Divide both sides by 1.25 to solve for $ x $: \[ x = \frac{20}{1.25} = 16 \] Thus, the value of $ x $ is 16, which corresponds to Option 2. **Explanation of Incorrect Options:** - **Option 1 (15):** - If $ x $ were 15, then the equation $ 20 = 15 \times 1.25 $ would not hold true, as $ 15 \times 1.25 = 18.75 $, which is not equal to 20. - **Option 3 (18):** - If $ x $ were 18, then the equation $ 20 = 18 \times 1.25 $ would not hold true, as $ 18 \times 1.25 = 22.5 $, which is not equal to 20. - **Option 4 (25):** - If $ x $ were 25, then the equation $ 20 = 25 \times 1.25 $ would not hold true, as $ 25 \times 1.25 = 31.25 $, which is not equal to 20. Therefore, Option 2 is the only correct answer, as it satisfies the condition given in the problem.

Question

Accepted Answer

To determine the value of $ x $ where the cost price of 20 articles is equal to the selling price of $ x $ articles with a profit of 25%, we need to follow these steps:

1. **Understanding the Profit Percentage:**
   - A profit of 25% means that the selling price (SP) is 125% of the cost price (CP).

2. **Setting Up the Equation:**
   - Let the cost price of one article be $ CP $.
   - Therefore, the cost price of 20 articles is $ 20 \times CP $.
   - The selling price of one article, considering a 25% profit, is $ 1.25 \times CP $.

3. **Relating Cost Price and Selling Price:**
   - According to the problem, the cost price of 20 articles is equal to the selling price of $ x $ articles.
   - Therefore, $ 20 \times CP = x \times 1.25 \times CP $.

4. **Solving for $ x $:**
   - Simplify the equation: $ 20 = x \times 1.25 $.
   - Divide both sides by 1.25 to solve for $ x $:
     $$
     x = \frac{20}{1.25} = 16
     $$

Thus, the value of $ x $ is 16, which corresponds to Option 2.

**Explanation of Incorrect Options:**

- **Option 1 (15):** 
  - If $ x $ were 15, then the equation $ 20 = 15 \times 1.25 $ would not hold true, as $ 15 \times 1.25 = 18.75 $, which is not equal to 20.

- **Option 3 (18):**
  - If $ x $ were 18, then the equation $ 20 = 18 \times 1.25 $ would not hold true, as $ 18 \times 1.25 = 22.5 $, which is not equal to 20.

- **Option 4 (25):**
  - If $ x $ were 25, then the equation $ 20 = 25 \times 1.25 $ would not hold true, as $ 25 \times 1.25 = 31.25 $, which is not equal to 20.

Therefore, Option 2 is the only correct answer, as it satisfies the condition given in the problem.