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The boy ans girls in a college are in the ratio 3: 2. If 20% of the

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New post 09 Jul 2018, 15:33
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The boy ans girls in a college are in the ratio 3: 2. If 20% of the boys and 25% of the girls are adults , the percentage of the students who are not adults ?

A) 52
B) 58
C) 78
D) 40
E) 60
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New post 09 Jul 2018, 17:18
Solving by substitution

Lets say there are 100 students in the class

The boys and girls are in the ratio 3:2 => 3x:5x with unknown multiplier 'x'

total number of students => 3x + 2x = 100

=> 5x = 100
=> x = 20

=> Number of boys in the class = 3x = 60
=> Number of girls in the class = 2x = 40

Number of boys who are adults = 20% of number of boys = \(\frac{20}{100}* 60\) = 12
Number of girls who are adults = 25% of number of girls = \(\frac{25}{100}* 40\) = 10

Total number of boys and girls who are adults = 12 + 10 = 22
Total number of boys and girls who are not adults = 100 - 22 = 78

Percentage of boys and girls who are not adults = \(\frac{78}{100}\) = 78%

Hence option C
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The boy ans girls in a college are in the ratio 3: 2. If 20% of the  [#permalink]

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New post 09 Jul 2018, 19:50
selim wrote:
The boy ans girls in a college are in the ratio 3: 2. If 20% of the boys and 25% of the girls are adults , the percentage of the students who are not adults ?

A) 52
B) 58
C) 78
D) 40
E) 60

I. Logic - 15 seconds
Boys, % NOT adult: (100 - 20) = 80%
Girls, % NOT adult: (100 - 25) = 75%

Percent of all students who are not adults? MUST be between 75% and 80%. One answer works

Answer C

II. Weighted averages

Method #1
(B:G) = (3:2), total ratio parts 5
Not adults = N.A.
B's "weight" = 3
G's "weight" = 2

(% N.A.)(Weight of B) + (% N.A.)(Weight of G) divided by ratio parts' total of 5

\(\frac{.8(3)+.75(2)}{5}=\frac{2.4+1.5}{5}=\frac{3.9}{5}=\)
\(\frac{39}{50}=\frac{78}{100}=78\) %

Method #2
Finally, you can weight the boys and girls by their percent of the population

(B:G) = (3:2), total of 5 parts
B = \(\frac{3}{5}\) = 60% = (.6 of all students)
G = \(\frac{2}{5}\) = 40% = (.4 of all students)

From above, take the percent of boys and girls who are NOT adults. Multiply B and G by their respective percent of the whole population. Add.

No need to divide. That's accounted for when you take the percent of the population.

\((.6)(.8) + (.4)(.75) = (.48 + .30) = 78\) %

ANSWER C
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Re: The boy ans girls in a college are in the ratio 3: 2. If 20% of the  [#permalink]

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New post 10 Jul 2018, 06:31
selim wrote:
The boy ans girls in a college are in the ratio 3: 2. If 20% of the boys and 25% of the girls are adults , the percentage of the students who are not adults ?

A) 52
B) 58
C) 78
D) 40
E) 60


Let there be 30 Boys and 20 girls in the college.

So, 6 boys are adults and 24 boys and not adults.
And, 5 girls are adults and 15 girls are not adults.

So, The No of students who are not adults are 39 students, or 78% of the students are not adults,m Answer must be (C)
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Re: The boy ans girls in a college are in the ratio 3: 2. If 20% of the  [#permalink]

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New post 14 Jul 2018, 18:35
selim wrote:
The boy ans girls in a college are in the ratio 3: 2. If 20% of the boys and 25% of the girls are adults , the percentage of the students who are not adults ?

A) 52
B) 58
C) 78
D) 40
E) 60


We can pick convenient numbers, letting the number of boys = 150 and the number of girls = 100, which satisfies the 3 : 2 ratio of boys to girls..

So 0.2 x 150 = 30 adult males and 0.25 x 100 = 25 adult females.

So we have 55 adults out of 250 total students.

So non-adults represent 195/250 = 78/100 = 78 percent of the total.

Answer: C
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The boy ans girls in a college are in the ratio 3: 2. If 20% of the  [#permalink]

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New post 18 Jul 2018, 03:54
selim wrote:
The boy ans girls in a college are in the ratio 3: 2. If 20% of the boys and 25% of the girls are adults , the percentage of the students who are not adults ?

A) 52
B) 58
C) 78
D) 40
E) 60


let's assume total number of girls and boys = 100, since 20% of the boys and 25 % girls are adults then 100-20= 80 boys and 100-25=75 girls are non adults.
Now, to find the percentage of the students who are not adults, simply calculate the average of 80+75/2 = 78 apprx.
Hence, the answer is (C).
:)
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