CRE 7 - Escalator | Time, Speed & Distance

Answer: 72

Explanation :

Speed of Akas while going upstairs = 3 + 2 = 5 s/s.

Time take to go up = 60/5 = 12 seconds.

Speed of Akas while going downstairs = 3 - 2 = 1 s/s.

Time take to come down = 60/1 = 60 seconds.

⇒ Total time taken by Akash = 12 + 60 = 72 seconds.

Hence, 72.

Answer: 96

Explanation :

Let Bobby's speed be "a" steps per second and escalator's speed be "x" steps per second.

When escalator is moving up, no. of steps 
N = 80a + 80x (Since Bobby is moving upwards, 80x will be added)

When escalator is moving down, no. of steps 
N = 120a - 120x (Since Bobby is moving upwards, 120x will be subtracted)

By equating the number of steps, 80a + 80x = 120a - 120x.

⇒ a = 5x

⇒ N = 80a + 80x = 80a + 16a = 96a

∴ Time taken when the escalator is stationary = 96a/a = 96 seconds.

Hence, 96

Answer: 40

Explanation :

No. of steps = 30 + (30/3)x (Since Bobby is moving in the same direction, 10x will be added)

No. of steps = 32 + (32/4)x (Since Arpit is moving in the same direction, 8x will be added)

On equating the number of steps,

30 + 10x = 32 + 8x

x = 1 step per second.

Number of steps = 30 + (10 × 1) = 40 steps.

Hence, 40.

Answer: 40

Explanation :

Let the speed of Bunty and Bubli be 3a and 5a steps per second respectively.

Let "t" be the time taken to take by Bobby or Arpit to reach the other end.

For Bobby,
Number of steps = 3at + xt

For Arpit,
Number of steps = 5at – xt.

On equating the number of steps, we get

3at + xt = 5at – xt

∴ xt = at 

⇒ x = a.

When Bunty takes 30 steps, escalator would have moved 30/3a × x steps i.e. 30/3 = 10 steps

Therefore, the Number of Steps = 30 + (30x/3a) 

⇒ a = 30 + 10 = 40.

Hence, 40.

Answer: Option A

Explanation :

Both the person and the escalator are moving in the same direction. In this case, the relative speed would be Speed of (Man + Stairs).

We don’t know the speed of the escalator, so assume that to be e.

Let speed of P be 5a steps/sec and Q's is 3a steps/sec.

P is walking 50 steps and he does it in 50/5a = 10/a secs., but in this 10/a secs, even the escalator must have moved with speed "e". The length moved by it would be 10e/a.

So, we can say the total length is 50 + 10e/a (steps moved by P and the escalator helps P in reaching the top).

Similarly for Q we can write 40 + 40e/3a

Both are moving on the same escalator, hence total number of steps should be same.

50 + 10e/a = 40 + 40e/3a

So, e/a = 3

So total length is 50 + 10e/a = 80.

Hence, option (a).

Answer: 45

Explanation :

Take the length of the stairs LCM(90, 30) = 90

Time taken when going upstream is 90 sec, so we can say

M - E = 90/90 = 1

M + E = 90/30 = 3

So, speed of Man = 4/2 = 2

Time taken is 90/2 = 45 sec

Alternately,
When moving upstream speed is M + E

when moving when escalator is stopped is M

and when moving upstream speed is M - E

speed is in AP, so time will be in HP, since they are inversely proportional.

So, time taken would be -

2 × 90 × 30 / (90+30) = 60 × 90/120 = 45 secs.

Hence, 45.

Answer: Option C

Explanation :

A and B take 10 and 7 steps per second. Escalator takes 4 steps per second.

A is climbing down so effective speed is 10 – 4 =6 steps/sec

B is climbing up so effective speed is 7 + 4 = 11 steps/sec

They are moving in opposite directions so relative speed is 17 steps/sec.

As they meet in 5 sec, total steps = 17 × 5 = 85 steps.

Hence, option (c).

Answer: 10

Explanation :

Let us assume their speeds are 5s and 3s, and the speed of the escalator is 'x'.

Since both of them take the same time for the same distance, their effective speed is the same.

⇒ 5s - x = 3s + x

⇒ x = s

Speed of Shivam : Speed of escalator = 3s : s = 3 : 1

⇒ When Shivam takes 30 steps, the escalator takes 10 steps.

⇒ Total number of steps = 30 + 10 = 40 steps.

Both of them would have covered 20 steps when they crossed each other.

Shivam going up would have taken 15 steps, whereas the escalator would have taken 5 steps for him.

Atharva coming down would have taken 25 steps, out of which the escalator would have nullified the movement of 5 steps for him.

Difference in the number of steps = 25 - 15 = 10 steps.

Hence, 10.

Answer: Option B

Explanation :

Suppose, Shyam takes 1 min for every 3 steps, then he takes 1/3 min for every step.

For 25 steps, he takes 25/3 min, i.e. 8.33 min.

So, Vyom takes 1/2 min for every step.

For 20 steps, he takes 20/2 min, i.e. 10 min.

Difference between their times = 1.66 min

Escalator moves 5 steps (i.e. 25 steps of Shyam - 20 steps of Vyom) in 1.66 min.

Speed of escalator is 1 step for 0.33 min, i.e. 3 steps per minute (same as that of Shyam).

If escalator is moving, Shyam takes 25 steps and escalator also takes 25 steps.

Hence, total number of steps to be taken when escalator was turned off = 50.

Hence, option (b).

Answer: 42

Explanation :

Since the man’s wife is slower, she would have taken more number of steps if they were moving ‘against’ the escalator. But here the wife takes lesser no. of steps, therefore, they are moving ‘with the escalator, 

Let the man’s speed be 2v and wife’s speed be v. Let the speed of the escalator be u.

For man, number of steps = 28 + $\frac{28}{2v}\times u$

For woman, number of steps = 21 + $\frac{21}{v}\times u$

Now, total number of steps are equal in both cases.

⇒ 28 + $\frac{28}{2v}\times u$ = 21 + $\frac{21}{v}\times u$

Let u/v = a

⇒ 28 + 14a = 21 + 21a

⇒ a = 1 ∴ u = v.

⇒ Total number of steps = 21 + $\frac{21}{v}\times u$ = 21 + 21 = 42

Hence, 42.