Question

Two persons are climbing up on two moving escalators which have 120 steps. The ratio of 1st person’s speed to that of 1st escalator is 2:3 (steps). The ratio of 2nd person’s speed to that of escalator is 3:5 (steps). Find the total number of steps they both have taken together.

• A. 85
• B. 93
• C. 80
• D. 75

Answer 1

The Correct Option is B

Solution:

The problem involves two persons, each climbing a different escalator with 120 steps, and we need to find the total number of steps they climb together.

Let's solve it step-by-step:

1. First person's climb:
   • Let the speed of the first person be \(2x\) and the speed of the first escalator be \(3x\).
   • The combined speed \(= 2x + 3x = 5x\).
   • Time taken by the first person to climb 120 steps: \(\frac{120}{5x}\).
   • Steps taken by the first person = speed \(\times\) time = \(2x \times \frac{120}{5x} = \frac{240}{5} = 48\).
2. Second person's climb:
   • Let the speed of the second person be \(3y\) and the speed of the second escalator be \(5y\).
   • The combined speed \(= 3y + 5y = 8y\).
   • Time taken by the second person to climb 120 steps: \(\frac{120}{8y}\).
   • Steps taken by the second person = speed \(\times\) time = \(3y \times \frac{120}{8y} = \frac{360}{8} = 45\).
3. Total number of steps taken together:
   • Total steps \(= 48 + 45 = 93\).

The correct answer is:

93