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Football Team T has a total of 120 players, 40 percent of whom

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Football Team T has a total of 120 players, 40 percent of whom  [#permalink]

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New post 08 Oct 2018, 12:09
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E

Difficulty:

  65% (hard)

Question Stats:

56% (02:38) correct 44% (02:46) wrong based on 18 sessions

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Football Team T has a total of 120 players, 40 percent of whom are juniors. After the first game, the team had a certain number of injured players, 20 percent of whom were juniors. Juniors now make up 80 percent of the non-injured players. How many players other than juniors are injured?
A) 16
B) 24
C) 32
D) 45
E) 64

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Football Team T has a total of 120 players, 40 percent of whom  [#permalink]

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New post 08 Oct 2018, 13:41
Abhi077 wrote:
Football Team T has a total of 120 players, 40 percent of whom are juniors. After the first game, the team had a certain number of injured players, 20 percent of whom were juniors. Juniors now make up 80 percent of the non-injured players. How many players other than juniors are injured?
A) 16
B) 24
C) 32
D) 45
E) 64


Refer to the attached grid.

Let x be the number of injured
Let y be the number of not injured.

0.2x + 0.8y = 48 total number of juniors.
2x + 8y = 480
x + 4y = 240 (1)

Total number of not juniors

0.8x + 0.2y = 72
8x + 2y = 720
4x + y = 360

16x + 4y = 1,440 (2)

16x + 4y = 1,440
x + 4y = 240

(2) - (1) = 15x = 1,200

X = 80

0.8 * 80 = 64

Answer choice E

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Re: Football Team T has a total of 120 players, 40 percent of whom  [#permalink]

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New post 08 Oct 2018, 19:51
Total Number of Players=120
Juniors= 40% of 120=48
Let, Injured=x
Then, Juniors Injured= 20% of x=x/5
Seniors Injured=4x/5.........Eq1
Non injured players=120-x
Now, total junior players after injury=48-(x/5) [which is 80% of the total non injured players]
Total non injured=120-x
So, 48-(x/5)=80% of (120-x)
If we solve for x, we get x=80
From Eq1, we get, seniors injured= (4*80)/5=64 (E)

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Re: Football Team T has a total of 120 players, 40 percent of whom   [#permalink] 08 Oct 2018, 19:51
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Football Team T has a total of 120 players, 40 percent of whom

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