Sister's Ages Problem: Step-by-Step Solution

Let's break down this age problem step-by-step.

1. Define Variables for Sister's Ages

• Let the current age of Tejasvi be $T$ years.
• Let the current age of Trishana be $Tr$ years.
• Let the current age of Meena be $M$ years.

2. Use the Given Information to Form Equations

We are given:

• Tejasvi and Trishana are twins: $ T = Tr $. Let's use $x$ for their common age. So, $ T = x $ and $ Tr = x $.
• The sum of Tejasvi's and Trishana's ages is the same as Meena's age: $ T + Tr = M $. Substituting $x$, we get $ x + x = M $, which simplifies to $ M = 2x $.
• Four years earlier, the ratio of Tejasvi's age to Meena's age was 1:3.
  • Tejasvi's age 4 years ago: $ T - 4 = x - 4 $.
  • Meena's age 4 years ago: $ M - 4 = 2x - 4 $.
  • The ratio was: $ \frac{T - 4}{M - 4} = \frac{1}{3} $.

3. Solve the Age Ratio Equation

Substitute the expressions for Tejasvi's and Meena's ages 4 years ago into the ratio equation:

$ \frac{x - 4}{2x - 4} = \frac{1}{3} $

Cross-multiply to solve for $x$:

$ 3(x - 4) = 1(2x - 4) $

$ 3x - 12 = 2x - 4 $

Rearrange the terms to isolate $x$:

$ 3x - 2x = 12 - 4 $

$ x = 8 $

So, the current age of Tejasvi and Trishana is 8 years.

4. Calculate Trishana's Age in 4 Years

We need to find Trishana's age 4 years from now.

• Trishana's current age is $ x = 8 $ years.
• Trishana's age 4 years from now will be $ Tr + 4 = x + 4 $.
• Substituting the value of $x$: $ 8 + 4 = 12 $ years.

Therefore, Trishana will be 12 years old 4 years from now.