Arun and Bhadra are brothers. In how many years from now will Bhadra’s age be 50 years? I. The ratio of the current ages of Arun and Bhadra is 5:7 respectively. II. Bhadra was born 10 years before Arun. III. 5 years hence, Arun’s age would be three-fourth of Bhadra’s age at that time.

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Let Arun's current age be $A$ and Bhadra's current age be $B$. We need the number of years $t$ such that $B+t=50$, so $t=50-B$.

I & II:
- From I: $A=	frac{5}{7}B$. From II: $B=A+10$. 
- Substitute: $B=	frac{5}{7}B+10\Rightarrow B-	frac{5}{7}B=10\Rightarrow 	frac{2}{7}B=10\Rightarrow B=35$. 
- Hence $t=50-35=15$.

I & III:
- From I: $A=	frac{5}{7}B$. From III: $A+5=	frac{3}{4}(B+5)$.
- Substitute: $	frac{5}{7}B+5=	frac{3}{4}B+	frac{15}{4}$. 
- Rearranging: $(	frac{5}{7}-	frac{3}{4})B=	frac{15}{4}-5\Rightarrow -	frac{1}{28}B=-	frac{5}{4}\Rightarrow B=35$. 
- Hence $t=15$.

II & III:
- From II: $A=B-10$. From III: $A+5=	frac{3}{4}(B+5)$.
- Substitute: $B-10+5=	frac{3}{4}B+	frac{15}{4}\Rightarrow B-5=	frac{3}{4}B+	frac{15}{4}$.
- So $	frac{1}{4}B=	frac{35}{4}\Rightarrow B=35$. 
- Hence $t=15$.

Each pair of statements yields $B=35$, so any two of the three statements are sufficient to determine when Bhadra will be 50.

FINAL_ANSWER: a

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