Question

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?

• A. 105
• B. 150
• C. 135
• D. 120

Answer 1

The correct option is D 120

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