Katrina walks down an up-escalator and counts 150 steps. Priyanka walks up the same escalator and counts 75 steps. Katrina takes three times as many steps in a given time as Priyanka. How many steps are visible on the escalator?

105

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150

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135

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120

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Solution

The correct option is D 120
Total steps are constant. Taking speed of Katrina to Priyanka to escalator as 3:1:x
$\Rightarrow 150 - (\frac{150}{3}) \times x = 75 + (\frac{75}{1}) \times x \Rightarrow 150 - 50 x = 75 + 75 x \Rightarrow 75 = 125 x \Rightarrow x = \frac{3}{5}$
So steps $= 15 - \frac{150}{3} \times \frac{3}{5} = 120$

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Katrina walks down an up-escalator and counts 150 steps. Priyanka walks up the same escalator and counts 75 steps. Katrina takes three times as many steps in a given time as Priyanka. How many steps are visible on the escalator?

The correct option is D 120Total steps are constant. Taking speed of Katrina to Priyanka to escalator as 3:1:x ⇒150−(1503)×x=75+(751)×x⇒150−50x=75+75x⇒75=125x⇒x=35 So steps =15−1503×35=120