A football league consists of 800 total players, 65 percent of whom pl

Question

A football league consists of 800 total players, 65 percent of whom play on offense. If there are only offensive and defensive players in the league, how many defensive players would have to join for the defensive players to comprise at least 40 percent of the league? 
A) 63
B) 64 
C) 65 
D) 66 
E) 67

Archit3110 · Accepted Answer

total players = 800
offense players= 800*.65= 520

so now to make a team which has 40% defensive players ,keeping the count of offense players same i.e 520 it would be 60% of total league players

520= x* 60/100
x= 867

addition of players required = 867-800 
= 67
IMO E

KarishmaB · Answer

Currently there are 35% defensive players. Defensive players need to be added to get 40% defensive players.

w1/w2 = (100 - 40)/(40 - 35) = 12/1

So for 12 current players, we need to add 1 new defensive player.
For 800 correct players, we need to add 800/12 = 66.67 players i.e. 67 players 
The defensive players need to be at least 40%. If we add 67 players, they will be just above 40%.

Answer (E)

chetan2u · Answer

Another method..

65% means Offensive are  800\frac{65}{100}=520 ..

The ONLY change is in the number of Defensive player, so offensive players will remain the same as 520..
Say the new total is x.
But if D are atleast 40%, O will be at the most 60%, that is O \leq{\frac{60}{100}*x =>  520\leq{\frac{60}{100}*x =>  x\geq{520*100/60}......x\geq{866.66}

The number cannot be a decimal, so take the decimal as complete or 867..
The new player added = 867-800=67

E

cm291093 · Answer

Isn't the language of the question different? I mean how can someone deduce that this is the way this question has to be solved. By reading the question I never even thought of going this way. The thought that came to my mind was 35% is 280 , and 40% of league is 320. So 40 must be added to get atleast 40%.

APram · Answer

There must have been some mistakes that you came to such inference

The question simply asked how much more defence players are needed so that it becomes 40% of all atleast.

himssss29 · Answer

other explanations confused me a bit. Here's how I solved it-

Total 800,
Currently, offence- 520 (65%)
 defence- 280 (35%)

when the defence will raise up to 40%, the total will also rise

Therefore, 520/280+x= 60/40 (when the defence will rise up to 40%, offence will stay the same number as before)

1040=840+3x
200=3x
x=66.66 (Note that "atleast" this number will be needed)
Hence, E-67 is the correct answer

A football league consists of 800 total players, 65 percent of whom pl

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A football league consists of 800 total players, 65 percent of whom pl

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