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
$$\Rightarrow$$Â 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.
$$\Rightarrow$$Â 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.
$$\Rightarrow$$Â 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.
$$\Rightarrow$$Â 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
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