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03. The profit earned after selling an article for Rs. 650 is same as the loss incurred after selling the article for Rs. 426. Find the half of the 50% of the cost price.

a. Rs. 134.50

b. Rs. 135.50

c. Rs.146.50

d. Rs.125.50

Let the cost price of the article be denoted by \( C \).

According to the problem, the profit earned by selling the article for Rs. 650 is equal to the loss incurred by selling it for Rs. 426. This gives us two conditions:

1. Profit = \( 650 - C \)
2. Loss = \( C - 426 \)

Since the profit equals the loss, we can set up the equation:

\[
650 - C = C - 426
\]

### Solving for \( C \):

\[
650 + 426 = 2C
\]
\[
1076 = 2C
\]
\[
C = \frac{1076}{2} = 538
\]

So, the cost price \( C \) is Rs. 538.

### Now, we need to find "half of the 50% of the cost price":

- 50% of the cost price: \( 50\% \times 538 = \frac{538}{2} = 269 \)
- Half of that: \( \frac{269}{2} = 134.50 \)

Thus, the answer is **Rs. 134.50**.

The correct option is **(a) Rs. 134.50**.

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Would you like more details or have any questions? Here are 5 related questions:

1. How do you calculate profit and loss percentage in business scenarios?
2. What is the formula for calculating the cost price if selling price and profit are given?
3. How do you calculate percentage discounts in sales problems?
4. What is the significance of cost price, selling price, and mark-up in profit analysis?
5. How do you determine break-even points in profit and loss scenarios?

**Tip:** When dealing with profit and loss problems, always establish a clear relationship between cost price, selling price, profit, and loss before solving.

The profit earned after selling an article for Rs. 650 is same as the loss incurred after selling the article for Rs. 426. Find the half of the 50% of the cost price.

a. Rs. 134.50
b. Rs. 135.50
c. Rs.146.50
d. Rs.125.50

Solve a profit and loss problem where the profit from selling an article at Rs. 650 equals the loss from selling it at Rs. 426. Learn to calculate the half of the 50% of the cost price using linear equations and percentages. Suitable for students in Grades 6-8.

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