Let: $x$ = number of persons who read magazine X only, $y$ = number of persons who read magazine Y only, $b$ = number of persons who read both magazines.

Step 1: Given Relationships

1. $x = 3y$ (number of persons who read X only is thrice those who read Y only).
2. $y = 3x$ (number of persons who read Y only is thrice those who read X only).

Step 2: Contradiction in Relationships The two conditions, $x = 3y$ and $y = 3x$, cannot hold simultaneously unless $x = 0$ and $y = 0$. Thus, we assume the problem compares relationships involving $b$.

Step 3: Check the Conclusions Conclusion 1: "The number of persons who read both magazines is twice the number of persons who read only magazine X." This implies: $b = 2x$

Conclusion 2: "The total number of persons who read either one magazine or both magazines is twice the number of persons who read both magazines." This implies: $x + y + b = 2b$

Step 4: Simplify and Verify From $x = 3y$, substitute into $x + y + b = 2b$: $3y + y + b = 2b$ $4y = b$

Check Conclusion 1: If $b = 4y$ and $x = 3y$, then: $b = 2x$ $4y = 2(3y)$ $4y = 6y$ (True)

Conclusion 2: $x + y + b = 2b$ $3y + y + 4y = 2(4y)$ $8y = 8y$ (True)

Final Answer: Both conclusions are correct. Correct Option: C (Both 1 and 2).