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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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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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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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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

1

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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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

2

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

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