Two people of different heights are walking in two different circles

Question

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

(A) 30

(B) 48

(C) 75

(D) 100

(E) 120

chetan2u · Answer

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

Posted from my mobile device

Sabbir22 · Answer

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)

Posted from my mobile device

AhmadAli250 · Answer

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

adstudy · Answer

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,
 
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, 
 
Hence, 5 step of S = 100
So, S = 20 --- (2)
Using (1) and (2)
 \frac{4*3*20}{5} 
 =48

Hence  B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Two people of different heights are walking in two different circles

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Two people of different heights are walking in two different circles

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards