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The ratio of boys to girls in Class A is 1 to 4, and that in Class B
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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
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16 Apr 2017, 22:23

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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

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

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

Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B
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15 Apr 2017, 02:48

1

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

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

Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B
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16 Apr 2017, 22:32

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Method 2:

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
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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
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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 considered 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

Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B
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13 Dec 2017, 17:23

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

We are given that the ratio of boys to girls in Class A is 1 to 4 and that the ratio in Class B is 2 to 5.

The ratio of boys to girls in class A = x : 4x

The ratio of boys to girls in class B = 2y : 5y

Since there are twice as many students in class A as in class B, we can create the following equation:

x + 4x = 2(2y + 5y)

5x = 14y

x = 14y/5

From the two earlier ratios, we see that the total number of boys in the combined class is (x + 2y) and the total number of girls in the combined class is (4x + 5y). Thus, the ratio of boys to girls in the combined class will be (x + 2y)/(4x + 5y). Substituting 14y/5 for x, we have:

The ratio of boys to girls in Class A is 1 to 4, and that in Class B
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Updated on: 12 Aug 2018, 15:10

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

A and B=number of total students in each class x=ratio of total boys to total students A=2B substituting, 2B*1/5+B*2/7=3B*x➡ x=8/35 ratio of total boys to total students 8/(35-8)=8/27=ratio of total boys to total girls C

Originally posted by gracie on 15 Dec 2017, 14:07.
Last edited by gracie on 12 Aug 2018, 15:10, edited 1 time in total.

Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B
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13 Jan 2018, 17:13

Hi All,

This question can be solved by TESTing VALUES. Before choose your values though, you have to note the ratios involved:

1) Class A has a ratio of boys:girls = 1:4. This means that there are 4 girls for every 1 boy (and that the total number of girls MUST be a multiple of 4 and the total number of students MUST be a multiple of 5). 2) Class B has a ratio of boys:girls = 2:5. This means that there are 5 girls for every 2 boys (and that the total number of boys MUST be a multiple of 2, the total number of girls MUST be a multiple of 5 and the total number of students MUST be a multiple of 7).

We're told that the total number of students in Class A is TWICE the total number of students in Class B. Thus, we need to TEST a multiple of 5 that is exactly TWICE a multiple of 7...

Let's TEST Class A = 70 students (14 boys and 56 girls) Class B = 35 students (10 boys and 25 girls)

By combining these two classes, we'll end up with 24 boys and 81 girls, giving us a ratio of 24:81. Since 24 and 81 are both multiples of 3, we can reduce this ratio to... 8:27

Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B
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19 Feb 2018, 03:21

Let total number of students in Class A be 2x. Total number of students in Class B is x. Class A girls to boys -> 1:4 Class B girls to boys -> 2:5 Therefore, Total number of boys: 1/5(2x) + 2/7(x) = 24x/35 Total number of girls: 4/5(2x) + 5/7(x) = 81x/35

Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B
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08 Aug 2018, 09:50

Guess # of students in class B is 140, hence that of in A will be 280. Boy/girls ratio in class a will be 56/224 and in class B will be 40/100 Overall ratio will be (56+40)/(224+100) which will reduce to 8/27