In a certain city there are five towers. Tower III is taller than tower II. Height of Tower V is the average of the height of towers I and IV. Height of Tower II is the average of the height of towers I and III. Height of Tower I is the average of the height of towers II and V. Which tower is the shortest?

Given,

Tower III is taller than tower II

$$\Rightarrow$$  III > II

Height of Tower II is the average of the height of towers I and III which means height of Tower II lies between towers I and III.

$$\Rightarrow$$  III > II > I .........(1)

Height of Tower I is the average of the height of towers II and V which means height of Tower I lies between towers II and V.

$$\Rightarrow$$  II > I > V ..........(2)

Height of Tower V is the average of the height of towers I and IV which means height of Tower V lies between towers I and IV.

$$\Rightarrow$$  I > V > IV .........(3)

Combining (1), (2), (3)

III > II > I > V > IV

$$\therefore\ $$Height of Tower IV is the shortest.

Hence, the correct answer is Option A