Solving Age Word Problems: Finding When One Person is Twice Another's Age

This problem asks us to find out how many years from now Jaya will be twice as old as her son Bharat. We are given their current ages.

Let's break down the information given:

• Jaya's current age is 36 years.
• Bharat's current age is 11 years.

We need to find the number of years that need to pass for Jaya's age to be exactly double Bharat's age. Let's represent the number of years that pass by the variable \(x\).

After \(x\) years:

• Jaya's age will be her current age plus \(x\), which is \(36 + x\) years.
• Bharat's age will be his current age plus \(x\), which is \(11 + x\) years.

The problem states that after \(x\) years, Jaya will be twice as old as Bharat. We can write this condition as an equation:

\(\text{Jaya's age after } x \text{ years} = 2 \times (\text{Bharat's age after } x \text{ years})\)

Substituting the expressions for their ages after \(x\) years, we get the equation:

\(36 + x = 2(11 + x)\)

Now, let's solve this linear equation for \(x\):

First, distribute the 2 on the right side of the equation:

\(36 + x = 2 \times 11 + 2 \times x\)

\(36 + x = 22 + 2x\)

Next, we want to isolate \(x\) on one side of the equation. Let's subtract \(x\) from both sides:

\(36 + x - x = 22 + 2x - x\)

\(36 = 22 + x\)

Now, subtract 22 from both sides to find the value of \(x\):

\(36 - 22 = 22 + x - 22\)

\(14 = x\)

So, after 14 years, Jaya will be twice as old as Bharat.

Verifying the Answer

Let's check if our value of \(x=14\) is correct:

• After 14 years, Jaya's age will be \(36 + 14 = 50\) years.
• After 14 years, Bharat's age will be \(11 + 14 = 25\) years.

Is Jaya's age (50) twice Bharat's age (25)?

\(2 \times 25 = 50\)

Yes, 50 is indeed twice 25. The condition is satisfied.

Therefore, in 14 years, Jaya will be twice as old as Bharat.