Understanding the Age Problem: Vishal and Saksham

This question asks us to find Vishal's age at a specific point in the future, based on given relationships between his and Saksham's ages at two different points in time. We are given information about their current ages and their ages after 8 years. We need to use this information to determine their current ages first, and then calculate Vishal's age after a total of 16 years (8 years from the present, and then 'further 8 years' after that).

Setting up Equations for Vishal and Saksham's Ages

Let's represent the current ages of Vishal and Saksham using variables:

• Let Vishal's current age be $V$ years.
• Let Saksham's current age be $S$ years.

From the question, we can form two equations based on the given information:

1. "Vishal is three times as old as Saksham."

   This translates to the equation: $$V = 3S \quad (Equation \; 1)$$

2. "After 8 years, he will be two times as old as Saksham."

   After 8 years, Vishal's age will be $V+8$ and Saksham's age will be $S+8$. The relationship given is: $$(V+8) = 2(S+8) \quad (Equation \; 2)$$

Solving for Present Ages of Vishal and Saksham

Now we can use these two equations to find the current ages, $V$ and $S$. We can substitute the value of $V$ from Equation 1 into Equation 2:

Substitute $V = 3S$ into $(V+8) = 2(S+8)$:

Now, let's solve for $S$:

Subtract $2S$ from both sides:

Subtract 8 from both sides:

So, Saksham's current age is 8 years.

Now, substitute the value of $S$ back into Equation 1 ($V = 3S$) to find Vishal's current age:

So, Vishal's current age is 24 years.

Calculating Vishal's Age After Further 8 Years

The question asks for Vishal's age after 'further 8 years'. This means 8 years after the point that was already 8 years in the future. In total, this point in time is $8 + 8 = 16$ years from the present.

Vishal's current age is 24 years.

Vishal's age after 16 years will be:

Therefore, Vishal's age after further 8 years (a total of 16 years from the present) will be 40 years.

Summary of Ages

Let's quickly summarize the ages at different points in time:

• Currently: Vishal = 24 years, Saksham = 8 years (24 is 3 times 8)
• After 8 years: Vishal = $24 + 8 = 32$ years, Saksham = $8 + 8 = 16$ years (32 is 2 times 16)
• After further 8 years (Total 16 years from present): Vishal = $32 + 8 = 40$ years, Saksham = $16 + 8 = 24$ years

The question specifically asks for Vishal's age after further 8 years, which is 40 years.

Using the values we found ($V=24, S=8$):

The final answer is Vishal's age after further 8 years, which is 40 years.

Revision Table: Age Problem Concepts

Additional Information: Solving Age Word Problems

Age word problems are common in mathematics and aptitude tests. They typically involve relationships between people's ages at different points in time (past, present, future). Here are some tips for solving them:

• Always define variables for the current ages of the people involved.
• Carefully read the relationships given and translate them into algebraic equations. Pay close attention to phrases like "times as old," "older than," "younger than," and specify the time frame (e.g., "5 years ago," "in 10 years").
• If the problem involves multiple time points, write expressions for the ages of everyone at each specific time point mentioned (e.g., if current age is $A$, age after $x$ years is $A+x$, age $y$ years ago was $A-y$).
• Set up equations based on the relationships given for each time point.
• Solve the system of equations to find the current ages.
• Once current ages are known, calculate the required age at the specific time mentioned in the final question.
• Always check your answers by plugging the calculated ages back into the original statements to ensure they hold true.