NIMCET 2009 Question Paper with solutions

Question : 67 of 120

Marks: +1, -0

Recently, while in Bengaluru, I decided to walk down the escalator of a tube station. I did some quick calculation in my mind. I found that if I walk down twenty-six steps, I require thirty seconds to reach the bottom. However, if I am able to step down thirty-four stairs I would only require eighteen seconds to get to the bottom. If the time is measured 'from the moment the top step begins to descend to the time I step off the last step at the bottom, what is the height of the stairway in steps?

Validate

Solution:

Let

x

be the number of steps in staircase.
Then,

\;{x-28}/{30}=\;{x-34}/{18}

⇒ \;\; \;{x-26}/{5}=\;{x-34}/{3}

⇒ \;\; 3 x-78=5 x-170

⇒ \;\; 2 x=92

⇒ \;\; x=46

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