# Escalator Math Problem - Math Puzzle

Math puzzles are challenges or problems that require a person to use mathematical concepts and skills to solve. They can be used to help develop mathematical abilities, such as problem-solving, critical thinking, and logical reasoning.

Here is an interesting math problem that requires a solid mathematical foundation to arrive at the solution.

Problem Details :

There is an escalator and 2 people move down it. A takes 50 steps and B takes 75 steps while the escalator is moving down. Given that the time taken by A to take 1 step is equal to the time taken by B to take 3 steps. Find the no. of steps in the escalator while it is stationary?

Solution

Let us say that the escalator moves at the rate of n steps per second. Let us also say A takes 1 step per second and B takes 3 steps per second.

Case 1: When A is coming down A will take 50 seconds to complete 50 steps. In 50 seconds, the escalator would have moved 50n steps. The total number of steps on the escalator can be represented as = 50 + 50n

Case 2: When B is coming down B will take 25 seconds to complete 75 steps In 25 seconds, escalator would have moved 25n steps. in this case Total number of steps on the escalator can be represented as = 75 + 25n

The total number of steps on the stationary escalator is a constant

combining case 1 and case 2, we can represent an equation like this

=> 50 + 50n = 75 + 25n => this is because the number of steps is constant

after solving this equation

=> 25n = 25=> n = 1

Total number of steps = 50 + 50 = 75 + 25 = 100

Watch the below video for a detailed explanation.