Solving Age Word Problems: Finding Malini's Current Age

This question is a classic age word problem that can be solved using linear equations. We are given information about the current ages of two people, Shipra and Malini, and a condition relating their ages in the future.

Understanding the Given Information about Ages

Let's break down the information provided:

• The sum of the current ages of Shipra and Malini is 65 years.
• After 5 years, Shipra's age will be 15 years more than Malini's age.

Our goal is to find Malini's current age.

Setting Up Equations for Current and Future Ages

Let's represent the unknown ages with variables:

• Let Shipra's current age be \(S\) years.
• Let Malini's current age be \(M\) years.

From the first piece of information, we can write our first equation:

Equation 1: The sum of their current ages is 65.

\(S + M = 65\)

Now, let's consider their ages after 5 years:

• Shipra's age after 5 years will be \(S + 5\) years.
• Malini's age after 5 years will be \(M + 5\) years.

The second piece of information states that after 5 years, Shipra's age will be 15 years more than Malini's age. We can write this as our second equation:

Equation 2: Shipra's age after 5 years is 15 more than Malini's age after 5 years.

\(S + 5 = (M + 5) + 15\)

Solving the System of Linear Equations

We now have a system of two linear equations with two variables:

1. \(S + M = 65\)
2. \(S + 5 = M + 5 + 15\)

Let's simplify Equation 2:

\(S + 5 = M + 20\)

Subtract 5 from both sides:

\(S = M + 15\)

This simplified equation tells us that Shipra is currently 15 years older than Malini, which makes sense because the age difference between two people remains constant over time. The difference between their ages after 5 years is given as 15 years, so their current age difference must also be 15 years.

Now we can use the substitution method to solve the system. Substitute the expression for \(S\) from the simplified Equation 2 (\(S = M + 15\)) into Equation 1 (\(S + M = 65\)):

\((M + 15) + M = 65\)

Combine the terms with \(M\):

\(2M + 15 = 65\)

Subtract 15 from both sides:

\(2M = 65 - 15\)

\(2M = 50\)

Divide by 2 to find the value of \(M\):

\(M = \frac{50}{2}\)

\(M = 25\)

So, Malini's current age is 25 years.

We can also find Shipra's current age using \(S = M + 15\):

\(S = 25 + 15\)

\(S = 40\)

Let's verify our answer using the original conditions:

• Current sum of ages: \(S + M = 40 + 25 = 65\). This matches the first condition.
• Ages after 5 years: Shipra's age will be \(40 + 5 = 45\). Malini's age will be \(25 + 5 = 30\).
• Difference after 5 years: \(45 - 30 = 15\). This matches the second condition.

The values satisfy both conditions, confirming our solution is correct.

Therefore, Malini's current age is 25 years.

Conclusion on Malini's Age

Based on the calculations, Malini's current age is 25 years.

Revision Table: Key Information on Age Problems

Additional Information on Solving Age Word Problems

Age word problems are common in quantitative aptitude tests. They typically involve setting up and solving linear equations. Here are a few more tips:

• Always define your variables clearly, stating what age (current, past, or future) each variable represents.
• Pay close attention to keywords like "sum," "difference," "times," "ago," "hence," "after," etc., as they indicate the mathematical operations needed.
• When dealing with future or past ages, remember that everyone's age changes by the same amount over the same period.
• If there are multiple people involved, you will usually need multiple equations.
• Always check your final answer by plugging the values back into the original problem statement to ensure all conditions are met.
• Practice with different variations of age problems, such as those involving ratios of ages or multiple time periods.

Solving age problems effectively relies on careful reading, accurate translation into algebraic equations, and precise solving of the resulting system of equations.