Question

The height of pole A is $ \dfrac{5}{6} $ of pole B, and the height of pole B is $ \dfrac{1}{2} $ of pole C. If the height of pole C is 72m, how tall is pole A?
A) 60m
B) 30m
C) 18m
D) 12m

Answer 1

Hint: We have been given the height of one pole and the dependency of other pole’s heights on it. We can use this dependency to form equations and then by substitution, find the required height of the pole A

Complete step by step solution:
We have been given:
The height of pole A is $ \dfrac{5}{6} $ of pole B
 $ \Rightarrow A = \dfrac{5}{6}B....(1) $
The height of pole B is $ \dfrac{1}{2} $ of pole C
 $ \Rightarrow B = \dfrac{1}{2}C....(2) $
The length of the pole C is given to be 72m
C = 72 m
Substituting this value in (2), we get:
 $
  B = \dfrac{1}{2} \times 72m \\
   \Rightarrow B = 36\;m \;
  $
Substituting the value of height of pole B in (1) so as to get the height of pole A, we get:
 $
  A = \dfrac{5}{6} \times 36m \\
  \Rightarrow A = 5 \times 6m \\
   \Rightarrow A = 30\;m \;
  $
Therefore, for the given heights of other poles, the height of pole A is 30 m
So, the correct answer is “30 m”.

Note: Here, the method used is called substitution method because we get the values of all the quantities necessary to find the required value and then by substituting those, we obtain the required answer.