Step-by-step Solution:

Logical Analysis

First, let's translate the initial information into mathematical relationships, using A, B, C, and D for the ages of Ajith, Babita, Chetu, and Das respectively.

• A = 3B


• D = 2C


• B > C

Our goal is to find a single, unique value for A.

Evaluating the Statements

• 
  Statement I alone ("Chetu is 10 yr old"):
  

  If C = 10, then from the initial info, D = 20 and we only know that B > 10. Since A = 3B, A's age could be 33 (if B=11), 36 (if B=12), etc. We cannot find a unique age. This statement is not sufficient.

  
  


• 
  Statement II alone ("Babita and Das are older than Chetu by the same number of years"):
  

  This translates to B - C = D - C, which simplifies to B = D. Combining this with the initial info gives A = 3B = 3D = 3(2C) = 6C. We still don't know the value of C, so we can't find A's age. This statement is not sufficient.

  
  


• 
  Statements I and II Together:
  

  From Statement II, we derived the relationship A = 6C. From Statement I, we are given the value C = 10. We can now combine them:

  
  A = 6 * 10 = 60
  

  This gives us a single, unique age for Ajith. Therefore, both statements together are sufficient.

  
  

Final Answer: The correct option is C. I and II.