Problem Solving

Q5 . A and B walk up an escalator. The escalator moves at a constant speed. A takes six steps for every four of B's step. A gets to the top of the escalator after having taken 50 steps , while B( Slower) takes only 40 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?
a. 80
b. 100
c. 120
d. 160
[spoiler]oa : b[/spoiler]

With speed of escalator as constant, The ratio of speeds of A & B are 6:4 = 3:2

When A reaches to the top of escalator, he has moved 50 steps. Thus, the number of steps, B walked are 50*2/3 = 33.33
Thus, B has to take 50-33.33 = 16.67 steps to reach to the top.
But B takes 40-33.33 = 6.67 steps only.
Thus remaining is the speed of escalator. i.e. 16.67-6.67 = 10 steps.
Thus Speed of B:Speed of Escalator = 6.67:10 = 2:3

Thus, Speed of A : Speed of B : Speed of Escalator = 3:2:3

Thus, Speed of A = Speed of Escalator.
This means that When escalator is not moving then A has to climb double the steps it moves when escalator is moving.

Thus, A&B have to walk up 50*2=100 steps.
OA=(b)

hemant_rajput wrote:Q5 . A and B walk up an escalator. The escalator moves at a constant speed. A takes six steps for every four of B's step. A gets to the top of the escalator after having taken 50 steps , while B( Slower) takes only 40 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?
a. 80
b. 100
c. 120
d. 160
[spoiler]oa : b[/spoiler]

A = A's rate, B = B's rate, and E = the escalator's rate.
B/E = B/A * A/E.
Since B travels 4 steps for every 6 steps that A travels:
B/A = 4/6 = 2/3.

We can plug in the answers, which represent the number of steps on the escalator.

Answer choice C: 120 steps
Since A travels 50 steps to reach the top, the escalator must travel 70 steps, for a total of 50+70 = 120 steps.
Thus:
A/E = 50/70 = 5/7.
B/E = B/A * A/E = 2/3 * 5/7 = 10/21 = 40/84.

Since B/E = 40/84, when B travels 40 steps to reach the top, the escalator travels 84 steps, for a total of 40+84 = 124 steps.
Not possible: the escalator contains only 120 steps.

Since the total number of steps traveled by B and the escalator must DECREASE, the correct answer must be SMALLER.
Eliminate C.

Answer choice B: 100 steps
Since A travels 50 steps to reach the top, the escalator must travel 50 steps, for a total of 50+50 = 100 steps.
Thus:
A/E = 50/50 = 1/1.
B/E = B/A * A/E = 2/3 * 1/1 = 2/3 = 40/60.

Since B/E = 40/60, when B travels 40 steps to reach the top, the escalator travels 60 steps, for a total of 40+60 = 100 steps.
Success!

The correct answer is B.

hemant_rajput wrote: If the escalator were turned off, how many steps would they have to take to walk up?
[/spoiler]

If the escalator moved k steps by the time B moved 40 steps, then total steps covered = 40+k
If hypothetically A were to move for the same time as B, then total steps covered when A walks = (6/4)*40+k =60+k. But A only moves 50 steps in reality; this means it walks for lesser time than B does.

So total number of steps on the escalator, N=40+k = 5/6 (60+k) => k=60 => N = 100

The Iceman wrote:

hemant_rajput wrote: If the escalator were turned off, how many steps would they have to take to walk up?
[/spoiler]

If the escalator moved k steps by the time B moved 40 steps, then total steps covered = 40+k
If hypothetically A were to move for the same time as B, then total steps covered when A walks = (6/4)*40+k =60+k. But A only moves 50 steps in reality; this means it walks for lesser time than B does.

So total number of steps on the escalator, N=40+k = 5/6 (60+k) => k=60 => N = 100

can you please explain how you come up with this equation"N=40+k = 5/6 (60+k)"

KA : adthedaddy

I don't understand the below step of your solution :

Thus Speed of B:Speed of Escalator = 6.67:10 = 2:3

You mean to say it's approx.

hemanthkumarmn wrote:KA : adthedaddy

I don't understand the below step of your solution :

Thus Speed of B:Speed of Escalator = 6.67:10 = 2:3

You mean to say it's approx.

6.67:10 = 6.67/10 = 0.67

If you convert 0.67 into fraction, it is 2/3 and 2/3 in ratio form is 2:3

Thus, 6.67:10 = 2:3