How to get the answer of the above question ? This question was asked for 2018 keam.

Please give the concept of formation the two equation in the given question .

To tackle the question from the 2018 KEAM exam, we first need to understand the context and the specific problem being presented. Typically, such questions involve forming equations based on given conditions or relationships. Let's break down the process of forming two equations step by step, using a hypothetical scenario to illustrate the concept.

Understanding the Problem

Imagine a scenario where you have two variables, say \( x \) and \( y \), representing two quantities. The question might provide certain relationships between these quantities, such as their sum, difference, or a ratio. The key is to extract these relationships clearly from the problem statement.

Identifying Relationships

Start by carefully reading the question to identify what is being asked. Look for keywords that indicate relationships:

• Sum: If the question states that the sum of two quantities is a certain value, you can write an equation like \( x + y = S \).
• Difference: If it mentions the difference, you might form an equation like \( x - y = D \).
• Product or Ratio: For products or ratios, you could have equations like \( xy = P \) or \( \frac{x}{y} = R \).

Formulating the Equations

Once you identify the relationships, you can start forming your equations. Let’s say the problem states:

• The sum of two numbers is 30.
• The difference between the two numbers is 10.

From this, you can derive the following equations:

• Equation 1: \( x + y = 30 \)
• Equation 2: \( x - y = 10 \)

Solving the Equations

With your two equations established, the next step is to solve them simultaneously. You can use methods such as substitution or elimination. For our example:

From Equation 1, you can express \( y \) in terms of \( x \):

y = 30 - x

Now, substitute this expression for \( y \) into Equation 2:

x - (30 - x) = 10

Simplifying this gives:

2x - 30 = 10

From here, you can solve for \( x \) and subsequently find \( y \).

Example Solution

Continuing from our simplification:

2x = 40

x = 20

Now substitute \( x \) back into the equation for \( y \):

y = 30 - 20 = 10

Thus, the two numbers are 20 and 10.

Final Thoughts

Forming equations from a word problem is a skill that improves with practice. Always look for the relationships between the quantities involved, and translate those relationships into mathematical expressions. With time, you’ll find that this process becomes more intuitive, allowing you to tackle even more complex problems with confidence.