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The ratio of the number of boys to that of girls in a school is 3:2. If 30% of boys and 70% of girls appeared in an examination, the ratio of students appeared in the examinations to that not appeared in the examination is
- a)23:27
- b)22:25
- c)21:17
- d)18:17
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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The ratio of the number of boys to that of girls in a school is 3:2. I...
Answer -A) 23: 27 Explanation : 3:2 = 30:20
30% boys = (30/100) × 30= 9 70% girls = (70/100) × 20 = 14 (9+14) : (50-23) = 23 : 27
30% boys = (30/100) × 30= 9 70% girls = (70/100) × 20 = 14 (9+14) : (50-23) = 23 : 27
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The ratio of the number of boys to that of girls in a school is 3:2. I...
Ratio of Boys to Girls
The given ratio of the number of boys to the number of girls in the school is 3:2. This means that for every 3 boys, there are 2 girls in the school.
Percentage of Boys and Girls Appeared in the Examination
Out of the total number of boys and girls in the school, 30% of boys and 70% of girls appeared in the examination.
Calculating the Ratio of Students Appeared and Not Appeared in the Examination
To find the ratio of students who appeared in the examination to those who did not appear, we need to compare the numbers.
Let's assume there are 3x boys and 2x girls in the school (since the ratio is given as 3:2).
- Boys Appeared: 30% of 3x = (30/100) * 3x = 0.9x
- Girls Appeared: 70% of 2x = (70/100) * 2x = 1.4x
- Boys Not Appeared: 3x - 0.9x = 2.1x
- Girls Not Appeared: 2x - 1.4x = 0.6x
Now, let's calculate the ratio of students who appeared to those who did not appear in the examination:
- Students Appeared: 0.9x + 1.4x = 2.3x
- Students Not Appeared: 2.1x + 0.6x = 2.7x
Hence, the ratio of students who appeared to those who did not appear in the examination is 2.3x:2.7x.
Simplifying the Ratio
To simplify the ratio, we can divide both sides by the common factor of x:
- Students Appeared: 2.3x ÷ x = 2.3
- Students Not Appeared: 2.7x ÷ x = 2.7
The simplified ratio becomes 2.3:2.7.
Converting the Ratio to Whole Numbers
To convert the ratio to whole numbers, we can multiply both sides by 10:
- Students Appeared: 2.3 * 10 = 23
- Students Not Appeared: 2.7 * 10 = 27
Therefore, the ratio of students who appeared in the examination to those who did not appear is 23:27.
Correct Answer:
The correct answer is option A) 23:27.
The given ratio of the number of boys to the number of girls in the school is 3:2. This means that for every 3 boys, there are 2 girls in the school.
Percentage of Boys and Girls Appeared in the Examination
Out of the total number of boys and girls in the school, 30% of boys and 70% of girls appeared in the examination.
Calculating the Ratio of Students Appeared and Not Appeared in the Examination
To find the ratio of students who appeared in the examination to those who did not appear, we need to compare the numbers.
Let's assume there are 3x boys and 2x girls in the school (since the ratio is given as 3:2).
- Boys Appeared: 30% of 3x = (30/100) * 3x = 0.9x
- Girls Appeared: 70% of 2x = (70/100) * 2x = 1.4x
- Boys Not Appeared: 3x - 0.9x = 2.1x
- Girls Not Appeared: 2x - 1.4x = 0.6x
Now, let's calculate the ratio of students who appeared to those who did not appear in the examination:
- Students Appeared: 0.9x + 1.4x = 2.3x
- Students Not Appeared: 2.1x + 0.6x = 2.7x
Hence, the ratio of students who appeared to those who did not appear in the examination is 2.3x:2.7x.
Simplifying the Ratio
To simplify the ratio, we can divide both sides by the common factor of x:
- Students Appeared: 2.3x ÷ x = 2.3
- Students Not Appeared: 2.7x ÷ x = 2.7
The simplified ratio becomes 2.3:2.7.
Converting the Ratio to Whole Numbers
To convert the ratio to whole numbers, we can multiply both sides by 10:
- Students Appeared: 2.3 * 10 = 23
- Students Not Appeared: 2.7 * 10 = 27
Therefore, the ratio of students who appeared in the examination to those who did not appear is 23:27.
Correct Answer:
The correct answer is option A) 23:27.
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