By selling a table for Rs. 56, gain is as much percent as its cost in rupees. What is the cost price?

Let the cost price of the table be \( x \) rupees.

The problem states that the gain percentage is equal to the cost price in rupees. Therefore, the gain percentage is \( x \% \).

Using the formula for selling price:
\[
\text{Selling Price} = \text{Cost Price} + \text{Gain}
\]
\[
\text{Selling Price} = x + \left( \frac{x \times x}{100} \right)
\]

Given that the selling price is Rs. 56, we can set up the equation:
\[
56 = x + \frac{x^2}{100}
\]

Now, multiplying through by 100 to eliminate the denominator:
\[
5600 = 100x + x^2
\]

Rearranging the equation:
\[
x^2 + 100x - 5600 = 0
\]

This is a quadratic equation. Solving it using the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
For the equation \( x^2 + 100x - 5600 = 0 \), \( a = 1 \), \( b = 100 \), and \( c = -5600 \).

Let's calculate the solution.

The solutions to the quadratic equation are \( x = 40 \) and \( x = -140 \). Since the cost price cannot be negative, the valid solution is \( x = 40 \).

Thus, the cost price of the table is Rs. 40.

Would you like more details or have any questions?

Here are 5 related questions to think about:
1. What would the selling price be if the gain percentage were doubled?
2. How would the equation change if the selling price was Rs. 70?
3. What happens to the cost price if the gain percentage is reduced by half?
4. How would you calculate the cost price if the gain was given in absolute terms instead of a percentage?
5. What is the impact of increasing the gain percentage on the cost price and selling price?

**Tip:** Always remember to keep track of units (like rupees) to avoid confusion in such problems.

Discover how to solve a quadratic equation to find the cost price when the selling price is Rs. 56, and the gain percentage equals the cost price in rupees. Learn key algebraic concepts and quadratic equation methods, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation