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Hovkial
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Two people of different heights are walking in two different circles 07 Oct 2019, 16:23
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95% (hard)

Question Stats:

38% (02:49) correct 63% (02:43) wrong based on 56 sessions

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Two people of different heights are walking in two different circles of the same radii. When the taller person walks three steps, the shorter person walks five steps in the same time. The distance traveled by the taller person in five steps is equal to the distance traveled by the shorter person in four steps. The shorter person completed walking 100 rounds. How many rounds did the taller person walk?

(A) 30

(B) 48

(C) 75

(D) 100

(E) 120
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B
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Two people of different heights are walking in two different circles 07 Oct 2019, 20:54
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Hovkial
Two people of different heights are walking in two different circles of the same radii. When the taller person walks three steps, the shorter person walks five steps in the same time. The distance traveled by the taller person in five steps is equal to the distance traveled by the shorter person in four steps. The shorter person completed walking 100 rounds. How many rounds did the taller person walk?

(A) 30

(B) 48

(C) 75

(D) 100

(E) 120

Let the taller be T and shorter be S.
Now the distance covered in 5 steps by T is equal to 4 steps by S.
So the distance per step by T:S is 4:5 or 4x:5x.

Also, T takes 3 steps in the time S takes 5 steps.
So S covers 5x*5 in the same time as T covers 4x*3.
If 5x*5=100 rounds, x=4.
Thus 12x=12*4=48 rounds.

B

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Two people of different heights are walking in two different circles 07 Oct 2019, 21:58
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For shorter person,
D/S = T or T=100/5 = 20
So the number of steps for taller one is 3*20 = 60
As the per the condition,
4/5 = x/60
Thus, x = 48 (B)

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Two people of different heights are walking in two different circles 10 Oct 2019, 13:59
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Let, n1 = # of rounds by person of short height = 100 (given) ; n2 = # of rounds by person of long height ; d1 = distance btw two adjacent steps of short-height person ; d2 = distance bwt two adjacent steps of long-height person.

Using formula, Total distance (D)= (# of rounds) * (# of steps) * (distance bwt two adjacent steps)

According to 2nd given condition, put it in above equation
=> n2*5*d2 = 100*4 *d1
=> n2*d2 = 80*d1 --------(1)

We can observe that # of steps are inversely proportional to distance between two adjacent steps.
=> d1/d2 = (# of steps of long-height person) / (# steps of short-height person) = 3/5 -------(2)

Put eq (2) in eq (1)
=> n2 = (80*3)/5 =48
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Two people of different heights are walking in two different circles 11 Oct 2019, 05:12
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Hovkial
Two people of different heights are walking in two different circles of the same radii. When the taller person walks three steps, the shorter person walks five steps in the same time. The distance traveled by the taller person in five steps is equal to the distance traveled by the shorter person in four steps. The shorter person completed walking 100 rounds. How many rounds did the taller person walk?

(A) 30

(B) 48

(C) 75

(D) 100

(E) 120

Hovkial
The distance traveled by the taller person in five steps is equal to the distance traveled by the shorter person in four steps.
Let taller person be T and shorter person be S;
Now,
5 steps of T = 4 steps of S
1 step of T = \(\frac{4}{5}\) steps of S
Also,
Hovkial
When the taller person walks three steps, the shorter person walks five steps in the same time
As,
1 step of T = \(\frac{4}{5}\) steps of S
3 step of T = \(\frac{4*3}{5}\) steps of S --- (1)
AND we also know,3 step of T = 5 step of S

Now we know,
Hovkial
The shorter person completed walking 100 rounds
Hence, 5 step of S = 100
So, S = 20 --- (2)
Using (1) and (2)
\(\frac{4*3*20}{5}\)
=48

Hence B
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