Solving the Age Word Problem

This problem involves finding the current ages of two people, Bipul and Saibal, based on given relationships between their ages now and in the future. We can solve this by setting up algebraic equations.

Defining Variables

Let's use variables to represent their current ages:

• Let Saibal's current age be $S$ years.
• Let Bipul's current age be $B$ years.

Forming Equations from the Given Information

We are given two pieces of information that can be translated into equations:

1. "Bipul is 16 years younger than Saibal."

   This means the difference between Saibal's age and Bipul's age is 16 years. Equation 1: $B = S - 16$

2. "12 years hence, Saibal's age will be 1.5 times that of Bipul."

   First, let's find their ages 12 years from now:

   • Saibal's age in 12 years = $S + 12$
   • Bipul's age in 12 years = $B + 12$

   The relationship given is that Saibal's future age is 1.5 times Bipul's future age. Equation 2: $S + 12 = 1.5 \times (B + 12)$

Solving the System of Equations

We have two equations with two variables:

• (1) $B = S - 16$
• (2) $S + 12 = 1.5(B + 12)$

We can substitute the expression for $B$ from Equation 1 into Equation 2.

Substitute $(S - 16)$ for $B$ in Equation 2:

$S + 12 = 1.5 \times ((S - 16) + 12)$

Simplify the expression inside the parenthesis:

$(S - 16) + 12 = S - 16 + 12 = S - 4$

Now substitute this back into the equation:

$S + 12 = 1.5 \times (S - 4)$

Distribute the 1.5 on the right side:

$S + 12 = 1.5S - 1.5 \times 4$

$S + 12 = 1.5S - 6$

Now, we need to isolate $S$. Let's subtract $S$ from both sides:

$12 = 1.5S - S - 6$

$12 = 0.5S - 6$

Add 6 to both sides:

$12 + 6 = 0.5S$

$18 = 0.5S$

To find $S$, divide both sides by 0.5 (or multiply by 2):

$S = \frac{18}{0.5}$

$S = 18 \times 2$

$S = 36$

So, Saibal's current age is 36 years.

We can also find Bipul's current age using Equation 1:

$B = S - 16$

$B = 36 - 16$

$B = 20$

Bipul's current age is 20 years.

Verification

Let's check if these ages satisfy the second condition for 12 years hence:

• Saibal's age in 12 years = $36 + 12 = 48$
• Bipul's age in 12 years = $20 + 12 = 32$

Is Saibal's future age 1.5 times Bipul's future age?

$1.5 \times 32 = 48$

Yes, $48 = 1.5 \times 32$. The ages satisfy both conditions.

Conclusion

Saibal is now 36 years old.

Revision Table: Age Problems and Equations

Additional Information: Solving Word Problems

Solving word problems often involves these steps:

• Read Carefully: Understand the problem and what is being asked.
• Define Variables: Assign letters to the unknown quantities you need to find.
• Translate to Equations: Write down mathematical equations that represent the relationships described in the problem.
• Solve the Equations: Use algebraic techniques to find the values of the variables.
• Check Your Answer: Plug the values back into the original problem statement or equations to make sure they make sense and satisfy all conditions.
• State the Final Answer: Clearly answer the specific question asked in the problem.

Age problems are a common type of word problem where the quantities change over time in a predictable way (by adding or subtracting years).