**Time Speed and Distance **

There is an escalator going up from the ground floor to the first floor. Varsha is climbing up the escalator while Sumit is climbing down (from the first floor to the ground floor) on the same escalator. On a stationary escalator, the time taken by Sumit to climb 8 steps is same as the time taken by Varsha to climb 6 steps. On the moving escalator, if Varsha takes 18 steps to reach the first floor while Sumit takes 60 steps to reach the ground floor, how many steps are there on the escalator?

**Suppose Varsha takes 3s steps per second and Sumit takes 4s step per second. **
**Let the speed of escalator be x steps/second .**
**Therefore the effective speed of Varsha = 3s + x and effective speed of Sumit 4s – x **
**Varsha takes 18 steps so time taken by Varsha to reach up = 18/3s = 6/s **
**Sumit takes 60 steps so time taken by Sumit to reach down 60/4s = 15/s **
**Together they cover equal number of steps ( as a resultant of their movement and the movement of their escalator )**
**S**_{Varsha}/S_{Sumit} = T_{Sumit}/T_{Varsha}= 2/5
**Suppose time taken by Sumit = 2t and the time taken by Raghu = 5t **
**2t ( x + 3s) = 5t ( 4s – x)**
**x = 2s**
**Varsha’s speed is 3s and speed of escalator = 2s . Therefore by time Varsha walks 18 steps the escalator takes 12 steps . Terefore the number of steps in the escalator = 18 + 12 = 30. **

**See our previous ‘Questions of the Day’:**

## 0 comments