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ashikaverma13
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quantumliner
Let us say

The Height from which the ball was first dropped as H0 = 248 feet
The Height reached by the ball after second bounce is H1
The Height reached by the ball after second bounce is H2 = 62 feet

Given , Height the ball reaches after bounce is a fraction of the height the ball reached in the previous bounce

The Height reached by the ball after second bounce = H2 = X of H1
==> 62 = X * H1 ...................Equation 1

The Height reached by the ball after first bounce = H1 = X of H0

==> H1 = X * 248 ...................Equation 2

Substituting value of H1 from Equation 2 to Equation 1

62 = X * H1 = X * X * 248

X^2 = 62/248 = 31/124 = 1/4

X = 1/2

Answer is A. 1/2


This can be solved by Geometric Progression formula as well

Term n = Term 1 * R ^ (n -1)

Here

R is nothing but the fraction, the question refers to

Term 1 is the Height from which the ball is dropped from = 248 feet
Term 2 is the Height reached by the ball after first bounce
.
.
.
Term n can be Term 3, which is the height the ball reached after the second bounce = 62 feet

Putting the above in equation

62 = 248 * x ^ (3-2)

62 = 248 * X ^ 2

62/248 = X ^ 2

X ^ 2 = 1/4

X = 1/2

Hey, thanks! I understood it now.

your clear explanation makes it so much simpler. much appreciated.
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ashikaverma13
A ball is dropped from 248 feet above the ground and after the second bounce it rises to the height of 62 feet. If the height to which the ball rises after each bounce is always the same fraction of the height reached on its previous bounce, what is this fraction?

A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6

I have an explanation but it's not quite clear. kindly explain your solution in detail. Thanks!

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An easy way I solved this: I noticed that 248 is 4x62. I rewrote it to the heights of 8 and 2 with 2 bounces. It was clear at this point that each bounce was reduced by 1/2.

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the question is telling that the height achieved by the ball after each bounce is in geometric progression.
248 X 62......
the option A satisfies this progression....
248/2= 124
124/2= 62
so 1/2 is the common ratio of the geometric progression.

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