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In a class, 60% of the students are boys and in an examination, 80% of the girls scored more than 40 marks(Maximum Marks:150). If 60% of the total students scored more than 40 marks in the same exam, what is the fraction of the boys who scored 40 marks or less.
- a)8/15
- b)7/15
- c)4/5
- d)1/5
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In a class, 60% of the students are boys and in an examination, 80% of...
Understanding the Problem
To solve this problem, let's break down the information given:
- **Total Students**: Let the total number of students be \( N \).
- **Boys**: 60% of \( N \) are boys, so the number of boys is \( 0.6N \).
- **Girls**: The remaining 40% are girls, giving \( 0.4N \) girls.
Girls Scoring More Than 40 Marks
- **Girls Scoring More**: 80% of the girls scored more than 40 marks. Thus, the number of girls who scored more than 40 marks is:
\[
0.8 \times 0.4N = 0.32N
\]
- **Girls Scoring 40 or Less**: The number of girls who scored 40 marks or less is:
\[
0.4N - 0.32N = 0.08N
\]
Total Students Scoring More Than 40 Marks
- **Total Students Scoring More**: 60% of all students scored more than 40 marks. Therefore:
\[
0.6N
\]
- **Boys Scoring More Than 40 Marks**: Since \( 0.32N \) girls scored more than 40 marks, the number of boys who scored more than 40 marks is:
\[
0.6N - 0.32N = 0.28N
\]
Calculating Boys Scoring 40 Marks or Less
- **Boys Scoring 40 or Less**: The number of boys who scored 40 marks or less is:
\[
0.6N - 0.28N = 0.32N
\]
Fraction of Boys Scoring 40 Marks or Less
- **Fraction Calculation**: To find the fraction of boys who scored 40 marks or less, we use:
\[
\text{Fraction} = \frac{\text{Boys scoring } 40 \text{ or less}}{\text{Total boys}} = \frac{0.32N}{0.6N} = \frac{0.32}{0.6} = \frac{32}{60} = \frac{8}{15}
\]
Thus, the fraction of boys who scored 40 marks or less is \( \frac{8}{15} \), which corresponds to option **A**.
To solve this problem, let's break down the information given:
- **Total Students**: Let the total number of students be \( N \).
- **Boys**: 60% of \( N \) are boys, so the number of boys is \( 0.6N \).
- **Girls**: The remaining 40% are girls, giving \( 0.4N \) girls.
Girls Scoring More Than 40 Marks
- **Girls Scoring More**: 80% of the girls scored more than 40 marks. Thus, the number of girls who scored more than 40 marks is:
\[
0.8 \times 0.4N = 0.32N
\]
- **Girls Scoring 40 or Less**: The number of girls who scored 40 marks or less is:
\[
0.4N - 0.32N = 0.08N
\]
Total Students Scoring More Than 40 Marks
- **Total Students Scoring More**: 60% of all students scored more than 40 marks. Therefore:
\[
0.6N
\]
- **Boys Scoring More Than 40 Marks**: Since \( 0.32N \) girls scored more than 40 marks, the number of boys who scored more than 40 marks is:
\[
0.6N - 0.32N = 0.28N
\]
Calculating Boys Scoring 40 Marks or Less
- **Boys Scoring 40 or Less**: The number of boys who scored 40 marks or less is:
\[
0.6N - 0.28N = 0.32N
\]
Fraction of Boys Scoring 40 Marks or Less
- **Fraction Calculation**: To find the fraction of boys who scored 40 marks or less, we use:
\[
\text{Fraction} = \frac{\text{Boys scoring } 40 \text{ or less}}{\text{Total boys}} = \frac{0.32N}{0.6N} = \frac{0.32}{0.6} = \frac{32}{60} = \frac{8}{15}
\]
Thus, the fraction of boys who scored 40 marks or less is \( \frac{8}{15} \), which corresponds to option **A**.
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Community Answer
In a class, 60% of the students are boys and in an examination, 80% of...
Assume Total no of students = 100
60% of the students are boys. so Boys=60,Girls=40
No. of girls who scored more than 40 marks = 80% of girls = 80% of 40 = 32.
No. of students who scored more than 40 marks = 60% of Total Students = 60
Therefore No. of boys who scored more than 40 marks = 60-32=28
No. of boys who scored less= Total boys – Boys(scored more) = 60-28=32
Fraction=(scored less)/Total boys = 32/60 =8/15
60% of the students are boys. so Boys=60,Girls=40
No. of girls who scored more than 40 marks = 80% of girls = 80% of 40 = 32.
No. of students who scored more than 40 marks = 60% of Total Students = 60
Therefore No. of boys who scored more than 40 marks = 60-32=28
No. of boys who scored less= Total boys – Boys(scored more) = 60-28=32
Fraction=(scored less)/Total boys = 32/60 =8/15
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In a class, 60% of the students are boys and in an examination, 80% of the girls scored more than 40 marks(Maximum Marks:150). If 60% of the total students scored more than 40 marks in the same exam, what is the fraction of the boys who scored 40 marks or less.a)8/15b)7/15c)4/5d)1/5Correct answer is option 'A'. Can you explain this answer?
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