Verbal Reasoning - Mental Ability Questions

Zenith means the time at which something is most powerful and Nadir means the lowest or most unsuccessful point in a situation. Both words are opposite to each other.

Genuine means authentic and phony means fraudulent or not genuine. Both are also opposite in meaning.

Zenith : Nadir :: Genuine : Phony

Modern is used to refer to something new whereas antiquated is used with respect to something old.

In other words, both terms are the opposite of each other.

From the above analysis, the missing word should be a word that represents the opposite of weak. Strong is used to with great influence. Therefore, the apt word is strong or any synonym of strong like potent, powerful, keen,...

Hence, Modern : Antiquated :: Weak : Strong.

Let Varun's age today = x years. 

Then, Varun's age after 1 year = (x + 1) years.

Therefore x + 1 = 2 (x - 12) =>  x + 1 = 2x - 24 =>  x = 25.