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The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink]

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14 Apr 2017, 16:14

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The ratio of boys to girls in Class A is 1 to 4, and that in Class B is 2 to 5. In addition, there are twice as many students in Class A as in Class B. If the two classes are combined to form one class, what would the resulting ratio of boys to girls?

A) 1 to 3 B) 5 to 12 C) 8 to 27 D) 6 to 25 E) 13 to 27

Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink]

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14 Apr 2017, 17:00

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We have three ratios:

1) Classroom A -> 1:4 -> potion of Boys = \(1/(1+4)\) = \(1/5\) 2) Classroom B -> 2:5 -> potion of Boys = \(2/(2+5)\) = 2/7 3) Classrooms RATIO -> 2:1 -> portion of Class A = 2/3 and portion of Class B = \(1/3\)

I stated the weighted portion of Boys in both classrooms:

Total Portion of Boys \(2/3*(1/5)+1/3*(2/7)\) \(= 2/3*(1/5+1/7)\) \(= 2/3*(12)/35\) \(= 8/35\)

Total Portion of Girls:

\(1-8/35=27/35\)

So the final ratio is Portion boys / Portion of girls 8/27

The ratio of boys to girls in Class A is 1 to 4, and that in Class B is 2 to 5. In addition, there are twice as many students in Class A as in Class B. If the two classes are combined to form one class, what would the resulting ratio of boys to girls?

A) 1 to 3 B) 5 to 12 C) 8 to 27 D) 6 to 25 E) 13 to 27

Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink]

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16 Apr 2017, 08:06

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amathews wrote:

The ratio of boys to girls in Class A is 1 to 4, and that in Class B is 2 to 5. In addition, there are twice as many students in Class A as in Class B. If the two classes are combined to form one class, what would the resulting ratio of boys to girls?

A) 1 to 3 B) 5 to 12 C) 8 to 27 D) 6 to 25 E) 13 to 27

Let's use weighted averages.

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

So, in this case, Weighted average of combined classes = (Class A proportion)(Class A average) + (Class B proportion)(Class B average)

CLASS A: Ratio of boys to girls in Class A is 1 to 4 So, for every 5 students, we have 1 boy and 4 girls. In other words, 1/5 of the students are boys. So, we can say the class A average is 1/5 boys

CLASS B: Ratio of boys to girls in Class B is 2 to 5 So, for every 7 students, we have 2 boys and 5 girls. In other words, 2/7 of the students are boys. So, we can say the class B average is 2/7 boys

There are twice as many students in Class A as in Class B. So, for every 3 students in the COMBINED group, there are 2 students from Class A, and 1 student from Class B In others words, Class A students comprise 2/3 of the COMBINED group, and Class B students comprise 1/3 of the COMBINED group

Now plug these values into our formula to get: Weighted average of combined classes = (2/3)(1/5) + (1/3)(2/7) = 2/15 + 2/21 = 14/105 + 10/105 = 24/105 = 8/35

So, in the combined group, 8/35 of the students are boys, which means 27/35 of the students are girls. In other words, among every 35 students in the combined group, 8 are boys and 27 are girls. So, the ratio of boys to girls = 8 to 27

The ratio of boys to girls in Class A is 1 to 4, and that in Class B is 2 to 5. In addition, there are twice as many students in Class A as in Class B. If the two classes are combined to form one class, what would the resulting ratio of boys to girls?

A) 1 to 3 B) 5 to 12 C) 8 to 27 D) 6 to 25 E) 13 to 27

There are several ways to do it. Let me discuss two of them.

Method 1:

• The ratio of the number of boys to girls in Class A is 1 : 4

o Therefore, we can say that the total number of students in Class A = 5x

• The ratio of the number of boys to girls in Class B is 2 : 5

o Therefore, we can say that the total number of students in Class B = 7y

• As per the given condition:

o \(5x = 2*7y\) o \(\frac{x}{y} = \frac{14}{5}\) o Take x = 14 and y = 5

Use the simple concept of weighted average to get the answer.

• The ratio of the number of boys to girls in Class A is 1 : 4

o Number of boys will be \(\frac{1}{(1+4)} = \frac{1}{5}th\) of total o Number of girls will be \(\frac{4}{(1+4)} = \frac{4}{5}th\) of total

• The ratio of the number of boys to girls in Class B is 2 : 5

o Number of boys will be \(\frac{2}{(2+5)} = \frac{2}{7}th\) of total o Number of girls will be \(\frac{5}{(2+5)} = \frac{5}{7}th\) of total

• Ratio of class A : Class B = 2 : 1

Thus weighted average = (Number of boys in Class A + Class B) / (Number of Girls in Class A + Class B) = \((2 * \frac{1}{5} + 1 * \frac{2}{7})/(2*\frac{4}{5} + 1 * \frac{5}{7})\) = \(\frac{24}{35}/\frac{81}{35}\) = \(\frac{8}{27}\)

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Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink]

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19 Apr 2017, 14:24

Another way of solving this. I believe this way is faster.

Class A: ratio a:4a and total student 5a ------------- Class B: ratio 2b:5b and total student 7b

as per question stem, 5a=2*(7b)

Ratio of the new class is (a+2b):(4a+5b) which same ratio as (5a+10b):(20a+25b) substitution leads to ratio 24b:81b or 24:81 Hence 8:27

Answer is C
_________________

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Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink]

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19 Apr 2017, 14:25

Another way of solving this. I believe this way is faster.

Class A: ratio a:4a and total student 5a ------------- Class B: ratio 2b:5b and total student 7b

as per question stem, 5a=2*(7b)

Ratio of the new class is (a+2b):(4a+5b) which same ratio as (5a+10b):(20a+25b) substitution leads to ratio 24b:81b or 24:81 Hence 8:27

Answer is C
_________________

What was previously thought to be impossible is now obvious reality. In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them

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