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If a group 305 of the men are more than 25 years old and 80% of the

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If a group 305 of the men are more than 25 years old and 80% of the  [#permalink]

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New post Updated on: 16 Nov 2019, 19:19
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In a group 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old.Twenty percent of all men play football. If 20% of the men above the age of 50 play football, what % of the players are less than or equal to 50 years ?

A)50
B)60
C)75
D)80
E)85

Originally posted by KSBGC on 16 Nov 2019, 02:25.
Last edited by chetan2u on 16 Nov 2019, 19:19, edited 1 time in total.
Corrected the Q and the OA
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If a group 305 of the men are more than 25 years old and 80% of the  [#permalink]

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New post 16 Nov 2019, 19:18
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KSBGC wrote:
If a group 305 of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old.Twenty percent of all men play football. If 205 of the men above the age of 50 play football, what % of the players are less than or equal to 50 years ?

A)50
B)60
C)75
D)80
E)85


Of course the question is faulty the way it is. It should be 30% and not 305 and 20% and not 205 as I believe instead of %, 5 has been written..

'30% of the men are more than 25 years old' is redundant information and can be discarded.

So we take total strength to be 100..
80 % or \(80\leq{50}\) yrs, so \(20>50\) yrs....
Now 20% of total play football, so 20 play football. Also 20% of >50yrs play football, that is 20% of 20 play football.
Thus, 20-4=16 players are less than or equal to 50 yrs..

% of the players are less than or equal to 50 years means 16 is what % of 20 = 100*16/20=80%.

OA given is also incorrect.
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If a group 305 of the men are more than 25 years old and 80% of the  [#permalink]

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New post 16 Nov 2019, 23:27
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KSBGC wrote:
In a group 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old.Twenty percent of all men play football. If 20% of the men above the age of 50 play football, what % of the players are less than or equal to 50 years ?

A)50
B)60
C)75
D)80
E)85


The highlighted part means that 20% of men who are above 50 play football.
Thus if total men are 100 then 20 are above 50. Hence 20% of 20 = \(\frac{20}{100} * 20\) = 4 men above 50 play football.
20% of total men means = \(\frac{20}{100} * 100 \)= 20 men play football.

So, 20 - 4 = 16 men under or equal to 50 play football.

\(\frac{16}{20} * 100\) = 80%

Answer D.
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If a group 305 of the men are more than 25 years old and 80% of the   [#permalink] 16 Nov 2019, 23:27
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