One ball will drop from a certain height. The height it will reach aft

Question

One ball will drop from a certain height. The height it will reach after rebounding from the floor is 60 percent of the previous height. The total travel is 292cm when it touches the floor on third time. What is the value of the original height? 
A. 80cm 
 B. 90cm 
 C. 100cm 
 D. 120cm 
 E. 130cm

*An answer will be posted in 2 days.

adiagr · Accepted Answer

when Ball comes down, Then i have indicated the distance covered in green
when Ball goes up, Then i have indicated the distance covered in red

Distance travelled uptil the ball touches the floor 3rd time:  h  +  0.6h  + 0.6 h  +  0.6*0.6 h  +  0.6*0.6 h

h + 2 * 0.6 * h + 2 * 0.36 * h = h (1+2*0.6+2* 0.36) = h (1+1.2+0.72) = 292

2.02 h = 292

h = 100.

C is the answer.

chetan2u · Answer

Hi,

we have to be careful to calculate the distance covered....
 two ways.. 
 1) let the distance be x... 
so first time it touches the floor - D = x...
next time it touches the floor, it travels .6x up and down - D = x+2*0.6x = 2.2x...
third time it touches the floor, it travels 0.6*0.6x up and down - D = 2.2x+2*0.6*0.6x = 2.92x...

so 2.92x = 292 ..... x =100

2) substitution.. 
start from middle value..
initial height = 100...
so in next jump it goes up 100*0.6 = 60 and in the third it moves 60*0.6 = 36..
so distance covered = 100+2*60+2*36 = 292..
this is what we are looking for..

rohit8865 · Answer

Let the ball dropped from height X cm

total distance in first trip = Xcm
second time bounces back to 60% of X(upwards) and again covers 60% of X(downwards)==2* 60% of X cm
third time also bounces back to 60% of 60% of X(upwards) and again covers 60% of 60%of X(downwards)=2* 60% of 60% of X cm
Given sum of all distance will be 292 cm
X +2*60%of X + 2*60% of 60% of X=292
X=100 cm
Ans C

Abhishek009 · Answer

Since percentage is rise is mentioned in the question stem it is best to assume , initial height as 100 and proceed ( rest will be easy) Next draw a mental image of the situation as below - Falling Ball.png First Drop Falling = 100 Total distance covered in first fall is 100 Second Drop Rise = 60 Fall = 60 Total distance covered in second fall is 120 Third Drop Rise = 36 Fall = 36 Total distance covered in second fall is 72 So, the total distance travelled in 292 (100+120+72) Hence answer will be (C)

MathRevolution · Answer

If we consider the initial height as x, then from x+2(60%)x+2(60%)^2(x)=292, we get x=100. Hence, the correct answer is C.

MidhilaMohan · Answer

Let X be the original height
After first touch it will traverse 0.6x up and 0.6x down
After second touch it will traverse 0.6*0.6x up and the same distance down
Hence total is
X+ 1.2x + 0.72x = 292
X=100

MHIKER · Answer

Rebounding; the ball go up and come back down.

Let original distance is x cm

x+2*0.60x+2*0.60*0.60x=292

x+1.20x+0.72x=292

2.92x=292

x=\frac{292}{2.92}=\frac{292}{292}*100=100

The answer is  C

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.

One ball will drop from a certain height. The height it will reach aft

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

One ball will drop from a certain height. The height it will reach aft

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