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A man visits a shopping mall almost every day and he walks up an up-going escalator that connects the ground and the first floor. If he walks up the escalator step by step it takes him 16 steps to reach the first floor. One day he doubles his stride length (walks up climbing two steps at a time) and it takes him 12 steps to reach the first floor.If the escalator stood still, how many steps would there be on sight?

A man visits a shopping mall almost every day and he walks up an up-going escalator that connects the ground and the first floor. If he walks up the escalator step by step it takes him 16 steps to reach the first floor. One day he doubles his stride length (walks up climbing two steps at a time) and it takes him 12 steps to reach the first floor.If the escalator stood still, how many steps would there be on sight?

Grade:10

8 Answers

sanatan sharma
26 Points
9 years ago

i am not sure but is the answer 48 ?

Krishnasankar S
16 Points
9 years ago

Is the answer 8???
I Found it in a crooky way..

Sathya
35 Points
9 years ago

Sanatsn sharma is absolutely right.Please explain it ....

Sathya
35 Points
9 years ago

@sanatan sharma:Which grade r u in ? R u going any coaching for iit jee?

sanatan sharma
26 Points
9 years ago

presently i am in grade 10   ;   going through the final examination phase 

yeah i am looking forward to some coaching for iitjee but the proposed present pattern has disturbed me.

the solution is :

first of all you must know the concept of escalators , as some steps from above disappear new ones appear from below thus the total no. of steps remain constant

the total height of the staircase = the man in first case took sixteen steps + the steps that disappeared in the time taken to cover the sixteen steps         [ assume the escalator to be still ]

                                                        = 16 + say x

in second case the total height of the staircase =  24 (since he took 2 steps at a time ) + 3x/4 (since the time is 12 steps)

equate both these 

you will get x as 32  and adding 16 you will get 48

now the assumption i have made is that the time taken to cover 2 steps at a time is th same as it takes to cover 1 step at a time

and in fact it is correct since 3x/4 would become  3x/2 thus resulting in negative values

Sathya
35 Points
9 years ago

But,What i dont understand is how did u get 3x/4 in the second case?

Sanandanan M
38 Points
9 years ago
in the first case, he had to climb 16 steps, and x steps disappeared in the second case, he had to climb 12 steps x for 16, x*(12/16) for 12 , that is 3x/4
rr
12 Points
6 years ago
The lcm(16,12) is 48

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