There are two escalators, one moving up and the other moving down at the same constant speed. Two individuals start at the top of each escalator, both walking down at a pace of 1 step per second. The person walking down the downward-moving escalator reaches the bottom after taking 20 steps. The person walking down the upward-moving escalator takes 60 seconds to reach the bottom. How many steps would each escalator have if they were stationary (i.e., paused)?

Escalator Steps | General | Trading Interview

Interview Questions Math Questions Escalator Steps

There are two escalators, one moving up and the other moving down at the same constant speed. Two individuals start at the top of each escalator, both walking down at a pace of 1 step per second.

The person walking down the downward-moving escalator reaches the bottom after taking 20 steps.
The person walking down the upward-moving escalator takes 60 seconds to reach the bottom.

How many steps would each escalator have if they were stationary (i.e., paused)?

Let's define the following:

T = Total number of steps on an escalator
S = Speed of the escalator in steps per second

Next, we can work this problem out using the following equations: \begin{equation} 20 = \frac{T}{S+1} \end{equation} The +1 in this equation accounts for the extra 1 step per second that the person is walking down. The second equation is: \begin{equation} 60 = \frac{T}{-S+1} \end{equation} Here, the S is negative, because the escalator is moving up instead of down. These two equations result in the following: \begin{equation} T = 20S + 20 \end{equation} \begin{equation} T = -60S + 60 \end{equation} Subtracting these two equations from each other results in \begin{equation} 0 = 80S - 40 \end{equation} \begin{equation} S = 0.5 \end{equation} If we substitute S in the first equation, we get that \begin{equation} 20 = \frac{T}{0.5+1} \end{equation} \begin{equation} T = 20*1.5 = 30 \end{equation} So, the escalator has 30 steps.

Correct Answer: 30

Python scratchpad

# Run Python right here in your browser
def two_sum(nums, target):
    seen = {}
    for i, n in enumerate(nums):
        if target - n in seen:
            return [seen[target - n], i]
        seen[n] = i
    return []

print(two_sum([2, 7, 11, 15], 9))  # [0, 1]

Run Python in your browser

Write and execute code — numpy, pandas & scikit-learn included — right on the question page.

My Notes

Notes are saved in this browser only. Sign up to keep them in your account.

Related Questions (79)

Title	Category	Subcategory	Difficulty	Status
Analog Clock Angle	Math Questions	General	Easy	Unlock with a membership
Area Between a Line and a Parabola	Math Questions	General	Easy	Unlock with a membership
Area of a Regular Hexagon	Math Questions	General	Easy	Unlock with a membership
Area of an Ellipse	Math Questions	General	Easy	Unlock with a membership
Area Under sin Squared	Math Questions	General	Easy	Unlock with a membership
Average Height of a Sine Arch	Math Questions	General	Easy	Unlock with a membership
Ball Inside a Cube	Math Questions	General	Easy	Unlock with a membership
Biking With Wind	Math Questions	General	Easy	Unlock with a membership
Birthday Candles	Math Questions	General	Easy	Unlock with a membership
Boats on a River	Math Questions	General	Hard	Unlock with a membership
Chessboard Crossing	Math Questions	General	Easy	Unlock with a membership
Choosing Blocks	Math Questions	General	Easy	Unlock with a membership
Circle Outside Its Inscribed Square	Math Questions	General	Easy	Unlock with a membership
Climbing 10 Stairs	Math Questions	General	Easy	Unlock with a membership
Cold Storage	Math Questions	General	Easy	Unlock with a membership
Cookie Sorting	Math Questions	General	Easy	Unlock with a membership
Counting Steps	Math Questions	General	Easy	Unlock with a membership
Diagonal of a Box	Math Questions	General	Easy	Unlock with a membership
Diagonals of a 20-Sided Polygon	Math Questions	General	Easy	Unlock with a membership
Factors of 2 in 100 Factorial	Math Questions	General	Easy	Unlock with a membership
Filling a Bathtub	Math Questions	General	Easy	Unlock with a membership
Fly vs Ant	Math Questions	General	Medium	Unlock with a membership
Games Played	Math Questions	General	Easy	Unlock with a membership
Going to the Beach #1	Math Questions	General	Medium	Unlock with a membership
How Many Dogs	Math Questions	General	Medium	Unlock with a membership
How Many Participants	Math Questions	General	Easy	Unlock with a membership
How Many Spiders	Math Questions	General	Easy	Unlock with a membership
How Many Tennis Matches	Math Questions	General	Easy	Unlock with a membership
How Often You Write the Digit 1	Math Questions	General	Easy	Unlock with a membership
Inflate Rate	Math Questions	General	Hard	Example
Integral of ln x	Math Questions	General	Medium	Unlock with a membership
Interview Permutations	Math Questions	General	Easy	Unlock with a membership
Jumping Frog	Math Questions	General	Medium	Unlock with a membership
Last Digit of 7 to the 2026th	Math Questions	General	Easy	Unlock with a membership
Last Two Digits of a Power of 3	Math Questions	General	Medium	Unlock with a membership
Length of a Chord	Math Questions	General	Easy	Unlock with a membership
Length of a Hanging Chain	Math Questions	General	Medium	Unlock with a membership
Length of the Curve y = x^(3/2)	Math Questions	General	Medium	Unlock with a membership
Log Base 2 of 100 Factorial	Math Questions	General	Hard	Unlock with a membership
Magic 37	Math Questions	General	Hard	Unlock with a membership
Maximum Intersections	Math Questions	General	Medium	Unlock with a membership
Multiples of 3 or 5 but Not Both	Math Questions	General	Easy	Unlock with a membership
Number of Digits of 7 to the 20th	Math Questions	General	Medium	Unlock with a membership
Number of Divisors of 720	Math Questions	General	Easy	Unlock with a membership
Number of Pigs	Math Questions	General	Easy	Example
Numbers Coprime to 100	Math Questions	General	Easy	Unlock with a membership
Numbers Without a 7	Math Questions	General	Easy	Unlock with a membership
Odd Numbers	Math Questions	General	Medium	Unlock with a membership
Painting Walls	Math Questions	General	Easy	Unlock with a membership
Patch of Lily Pads	Math Questions	General	Easy	Unlock with a membership
Paths Across a Grid	Math Questions	General	Easy	Unlock with a membership
Primes Between 100 and 130	Math Questions	General	Medium	Unlock with a membership
Product Around a Hundred	Math Questions	General	Easy	Unlock with a membership
Product of Three Primes	Math Questions	General	Easy	Unlock with a membership
Radius of a Circle	Math Questions	General	Hard	Unlock with a membership
Rectangles On Chessboard	Math Questions	General	Easy	Unlock with a membership
Remainder of 2 to the 100th Divided by 7	Math Questions	General	Easy	Unlock with a membership
River Length #1	Math Questions	General	Medium	Unlock with a membership
River Length #2	Math Questions	General	Medium	Unlock with a membership
Sequences	Math Questions	General	Easy	Unlock with a membership
Set of Distinct Integers	Math Questions	General	Easy	Unlock with a membership
Sharing a Glass	Math Questions	General	Easy	Unlock with a membership
Sheep Runs Home	Math Questions	General	Hard	Unlock with a membership
Smaller Cubes	Math Questions	General	Medium	Unlock with a membership
Spread Set	Math Questions	General	Hard	Unlock with a membership
Square of 9995	Math Questions	General	Easy	Unlock with a membership
Squares On Chessboard	Math Questions	General	Medium	Unlock with a membership
Squares or Cubes up to 10,000	Math Questions	General	Medium	Unlock with a membership
Subsets With an Even Sum	Math Questions	General	Medium	Unlock with a membership
Sum of All Digits up to 999	Math Questions	General	Medium	Unlock with a membership
Sum of the Divisors of 100	Math Questions	General	Medium	Unlock with a membership
Sum of Three Unit Fractions	Math Questions	General	Medium	Unlock with a membership
Summing 11 to 20	Math Questions	General	Easy	Unlock with a membership
Tic Tac Toe	Math Questions	General	Easy	Unlock with a membership
Triangle on Circle	Math Questions	General	Medium	Unlock with a membership
Unfolded Box	Math Questions	General	Hard	Unlock with a membership
Upstream or Downstream	Math Questions	General	Medium	Unlock with a membership
Volume of a Paraboloid	Math Questions	General	Easy	Unlock with a membership
Zeros at the End of 200 Factorial	Math Questions	General	Easy	Unlock with a membership

Discussion

Please log in to see the discussion.

Back to all Questions

The Interview Guide for Quants and Traders

Escalator Steps

What do you think of this page?