# CRE 7 - Escalator | Arithmetic - Time, Speed & Distance

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**CRE 7 - Escalator | Arithmetic - Time, Speed & Distance**

An escalator having 60 steps is moving up at the speed of 2 steps/second. Aakash has to go to first floor and come back on this escalator. Calculate time taken by Akash, if his speed on stationery escalator is 3 steps/second.

Answer: 72

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**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.

Workspace:

**CRE 7 - Escalator | Arithmetic - Time, Speed & Distance**

Bobby is going up the escalator. It takes Bobby 80 seconds to walk up the escalator which is moving upwards and 120 seconds to walk up the escalator which is moving downwards. Calculate the time (in secs) taken by Bobby to climb the escalator which is stationary.

Answer: 96

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**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

Workspace:

**CRE 7 - Escalator | Arithmetic - Time, Speed & Distance**

Bobby and Arpit are climbing on a moving escalator that is going up. Bobby takes 30 steps to reach the top but Arpit takes 32 steps to reach the top. Bobby can take 3 steps in a second while Arpit can take 4 steps in a second. Calculate the total number of steps in the escalator.

Answer: 40

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**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.

Workspace:

**CRE 7 - Escalator | Arithmetic - Time, Speed & Distance**

Bunty is climbing up the moving escalator that is going up and he takes 30 steps to reach the top while Bubli is coming down the same escalator. The speed’s ratio of Bunty and Bubli is 3 : 5. Calculate the number of steps if it’s given that both of them take same time to reach the other end.

Answer: 40

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**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.

Workspace:

**CRE 7 - Escalator | Arithmetic - Time, Speed & Distance**

P and Q walk up a moving up escalator at constant speeds. For every 5 steps that P takes Q takes 3 steps. How many steps would each have to climb when the escalator is switched off, given that P takes 50 and Q takes 40 steps to climb up the moving up escalator respectively?

- (a)
80

- (b)
90

- (c)
100

- (d)
None of these

Answer: Option A

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**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).

Workspace:

**CRE 7 - Escalator | Arithmetic - Time, Speed & Distance**

Anand takes 90 secs to move up an escalator which is moving downward and he takes 30 secs to move down the same escalator. How much time (in seconds) will he take to go up or down, when the escalator is switched off?

Answer: 45

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**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.

Workspace:

**CRE 7 - Escalator | Arithmetic - Time, Speed & Distance**

A can take 10 steps per second and B can take 7 steps per second. A mischievously starts climbing down an escalator that is moving upwards and at the same instant B starts climbing up the same escalator. They meet after 5 seconds. If the escalator works at a steady rate of 4 steps per second then how many steps are visible when the escalator is stopped?

- (a)
90

- (b)
80

- (c)
85

- (d)
None of these

Answer: Option C

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**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).

Workspace:

**CRE 7 - Escalator | Arithmetic - Time, Speed & Distance**

Shivam is climbing on a moving escalator that is going up and takes 30 steps to reach the top. Atharva on the other hand is coming down on the same escalator. For every 5 steps that Atharva takes, Shivam takes only 3 steps. Both of them take the same amount of time to reach the other end. What is the difference in the number of steps that both of them had taken when they crossed each other?

Answer: 10

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**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.

Workspace:

**CRE 7 - Escalator | Arithmetic - Time, Speed & Distance**

Shyam and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyam takes three steps for every two steps of Vyom. Shyam gets to the top of the escalator after taking 25 steps, while Vyom takes only 20 steps to reach the top. If the escalator was turned off, then how many steps would they have to take to walk up to the top?

- (a)
40

- (b)
50

- (c)
60

- (d)
75

- (e)
80

Answer: Option B

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**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).

Workspace:

**CRE 7 - Escalator | Arithmetic - Time, Speed & Distance**

A man and his wife walk up a moving escalator. The man walks twice as fast as his wife. When he arrives at the top, he has taken 28 steps. When she arrives at the top, she has taken 21 steps. How many steps are visible in the escalator at any one time.

Answer: 42

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**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.

Workspace:

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