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The average age of boys in a class is 15.4

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The average age of boys in a class is 15.4 [#permalink]

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The average age of boys in a class is 15.4, while that of girls in the same class is 14.4. If the average of the class is 14.8, what is the ratio of boys to girls in the class?
A) 1:3
B) 1:2
C) 2:1
D) 2:3
E) 3:2
[Reveal] Spoiler: OA

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Re: The average age of boys in a class is 15.4 [#permalink]

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New post 26 Feb 2016, 00:54
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Answer = D = 2:3

Simple Method (Using Alligation)

Avg Boys ............... Avg Girls

15.4 ........................ 14.4

................ 14.8 .............. (Class Avg)


= (14.8-14.4=0.4) ................ = (15.4-14.8 = 0.6)

\(Ratio = \frac{0.4}{0.6} = \frac{2}{3}\)
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Re: The average age of boys in a class is 15.4 [#permalink]

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New post 26 Feb 2016, 01:04
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Algebric Method:

Let the number of boys = x

\(\frac{b_1 + b_2 + ..... + b_x}{x} = 15.4\) ................... (1)

Let the number of girls = y

\(\frac{g_1 + g_2 + ........ + g_y}{y} = 14.4\) .................. (2)

Class average \(= \frac{b_1 + b_2 + ........ +b_x + g_1 + g_2 + ..... + g_y}{x+y} = 14.8\) ............... (3)

Placing values of (1) and (2) in equation (3)

\(\frac{15.4x + 14.4y}{x+y} = 14.8\)

\(\frac{x}{y} = \frac{2}{3}\)

Answer = D
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Re: The average age of boys in a class is 15.4 [#permalink]

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New post 08 Aug 2016, 18:11
Hi!
Experts : chetan4u , bunuel , magoosh, empowergmat, ... i tried to solve ad took 2 mins 20 seconds..
made estimate as ration of girls has to be higher .. reason: weight is inclined towards girls..
rest solved three option.
kindly share some other quick method which can save time please.
Thnaks

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The average age of boys in a class is 15.4 [#permalink]

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New post 08 Aug 2016, 20:04
let b=#boys
g=#girls
15.4b+14.4g=14.8(b+g)
b/g=2/3
b:g=2:3

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The average age of boys in a class is 15.4 [#permalink]

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New post 10 Dec 2016, 01:44
chetan2u wrote:
The average age of boys in a class is 15.4, while that of girls in the same class is 14.4. If the average of the class is 14.8, what is the ratio of boys to girls in the class?
A) 1:3
B) 1:2
C) 2:1
D) 2:3
E) 3:2

\(154b + 144g = 148 ( b + g )\)

\(154b + 144g = 148b + 148g\)

Or, \(154b - 148b = + 148g - 144g\)

Or, \(6b = 4g\)

Or, \(\frac{b}{g} = \frac{4}{6}\) = \(2:3\)

Hence, correct aswer will be (D) \(2:3\)
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The average age of boys in a class is 15.4 [#permalink]

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New post 17 Dec 2016, 12:21
Boys Avg age : 15.4 = 15 + 0.4
Girls Avg age : 14.4 = 14 + 0.4
I assumed
Boys : Girls = 15x : 14x
x = 4
60 : 70
6:7
I just choose 2:3

Can i solve something like this?
However, other's explanations make sense
Thanks
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Re: The average age of boys in a class is 15.4 [#permalink]

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New post 05 Aug 2017, 20:45
Excellent Question chetan2u

Here is my approach -->
Let the number of Boys be \(B\)
Let the number of Girls be \(G\)
Hence we need \(B:G\)

Sum(Age's of all boy's)=> \(15.4B\)
Sum(Age's of all Girl's)=\(14.4G\)

Now
Mean of the total class => \(\frac{15.4B+14.4G}{B+G} =14.8\)
Hence \(0.6B=0.4G\)
or\(\frac{B}{G}= \frac{2}{3}\)

Hence the Ratio=> \(2:3\)

Hence D

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The average age of boys in a class is 15.4 [#permalink]

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New post 06 Aug 2017, 14:18
This can be solved using a line

Avg (Boys) = 15.4 , Avg (Girl) = 14.4 , Avg (Class) = 14.8

14.4..14.6..14.8..15.0..15.2..15.4

Parts in ratio for girls = 14.8-14.4 = 0.4
Parts in ratio for girls = 14.8-15.4 = 0.6

\(\frac{0.4}{0.6}\)= \(\frac{2}{3}\)

Since the class average is closer to girls average, their weightage is higher. Reverse the fraction which is now the ratio 2:3

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The average age of boys in a class is 15.4   [#permalink] 06 Aug 2017, 14:18
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