Step-by-step Solution:

Quick Solution

We can solve this easily by translating the word problem into two algebraic equations.

1. Set Up the Equations

- Let Radha's present age be Rh and Rita's present age be Rt.

- From the first statement, "Radha is twice as old as Rita was 2 years ago":
Rh = 2 × (Rt - 2) --- (Equation 1)

- From the second statement, "If difference between their ages is 2 years" (implying Radha is older):
Rh - Rt = 2, which can be rearranged to Rh = Rt + 2 --- (Equation 2)

2. Solve the Equations

- Since both equations are expressions for Rh, we can set them equal to each other:
2 × (Rt - 2) = Rt + 2

- Now, solve this equation to find Rt (Rita's age):
2Rt - 4 = Rt + 2
2Rt - Rt = 2 + 4
Rt = 6 years old.

- Finally, use Equation 2 to find Radha's age:
Rh = Rt + 2 = 6 + 2 = 8 years old.

3. Verification (Optional)

- Let's check our answer. If Radha is 8 and Rita is 6, the age difference is 2 years. Two years ago, Rita was 4. Radha's age (8) is indeed twice Rita's age from 2 years ago (4). The solution is correct.

Final Answer: Radha is 8 years old today.