Q30 of 180 Page 1

A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2.5 m apart. What is the length of the wood required for the rungs?

The diagram is shown below.


It is given that,


The distance between two adjacent rungs = 25 cm.


The distance between topmost and bottommost rungs = 2.5m = 250 cm.



⇒ Total number of rungs =


Length of the bottom most rung = 45 cm and,


Length of the top most rung = 25 cm


And the length decreases uniformly from top to bottom. It is forming a finite series AP.


⇒ Required answer = , a = first term, l = last term


⇒


⇒


⇒ 385 cm = 3.85 m


Hence, length of wood required is 3.85 m.


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