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

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One ball will drop from a certain height. The height it will reach aft  [#permalink]

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New post 21 Jun 2016, 17:28
3
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

65% (02:21) correct 35% (02:23) wrong based on 131 sessions

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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.
Spoiler: OA

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Re: One ball will drop from a certain height. The height it will reach aft  [#permalink]

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New post 21 Jun 2016, 20:30
MathRevolution wrote:
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.


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..
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Re: One ball will drop from a certain height. The height it will reach aft  [#permalink]

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New post 21 Jun 2016, 22:25
1
MathRevolution wrote:
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.


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.
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Re: One ball will drop from a certain height. The height it will reach aft  [#permalink]

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New post 22 Jun 2016, 10:20
MathRevolution wrote:
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.

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
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Re: One ball will drop from a certain height. The height it will reach aft  [#permalink]

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New post 22 Jun 2016, 12:34
1
MathRevolution wrote:
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.


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 -

Attachment:
Falling Ball.png
Falling Ball.png [ 4.34 KiB | Viewed 3251 times ]


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)
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Re: One ball will drop from a certain height. The height it will reach aft  [#permalink]

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New post 26 Jun 2016, 07:26
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.
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Re: One ball will drop from a certain height. The height it will reach aft  [#permalink]

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Re: One ball will drop from a certain height. The height it will reach aft   [#permalink] 16 Aug 2017, 03:54
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