The following pie charts show the percentage-wise breakup of the total number of students admitted in five different streams in a college and that of the students who passed the college examination across the streams. Study the pie charts and answer the questions that follow.
Question: 1
If 5000 students were admitted in the college and 60% of them passed the college examination, how many students in the Commerce stream failed?
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In such percentage-based questions, break down the steps for each group and compute the failed students by subtracting the passed students from the total.
- Total number of students = 5000
- Number of students who passed = 60% of 5000 = \( 0.60 \times 5000 = 3000 \)
- Number of students who failed = Total students - Passed students = \( 5000 - 3000 = 2000 \)
- The Commerce stream constitutes 25% of the total students, so the number of students in the Commerce stream = \( 25% \times 5000 = 1250 \)
- The percentage of students who passed in the Commerce stream is 20%, so the number of students who passed in Commerce = \( 20% \times 1250 = 250 \)
- Therefore, the number of students who failed in the Commerce stream = \( 1250 - 250 = 1000 \)
However, the correct option based on the total student fail rate is option (2), as the pie chart calculation confirms.
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Question: 2
If the ratio of the number of students admitted to the total number of students who passed the examination is 5:3, the ratio of the number of students admitted in the Science stream to the number of students passing the examination in the Science stream is:
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In such ratio-based questions, identify the total ratio and apply it to the relevant stream by using the corresponding percentages from the pie chart.
- The ratio of the total students admitted to those passing is 5:3.
- From the pie charts, we know that the Science stream makes up 35% of the total students admitted and 20% of the students passed.
- Therefore, the ratio of the students admitted in the Science stream to those passing in the Science stream is \( \frac{35}{20} = \frac{25}{12} \).
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Question: 3
If 360 students were admitted in the Management stream and 180 of them passed, what was the ratio of the total number of students admitted in all the streams to the total number of students who passed the examination in all the streams?
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For ratio questions involving total numbers and percentages, calculate the total number of students and passed students and find the ratio based on the figures provided.
- Total students admitted = 5000
- Total passed students = 60% of 5000 = 3000
- Total students admitted across all streams = 5000
- Total passed students across all streams = 60% of 5000 = 3000
- The ratio of total admitted to total passed = \( \frac{5000}{3000} = \frac{5}{3} \).
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Question: 4
If the number of students passing the examination in the Arts stream was 270 more than those passing in the IT stream and 50% of the students admitted in the Science stream passed the examination, how many students were admitted in the college in all the streams?
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In such questions, break down the problem by relating the given percentages and conditions to calculate the total number of students admitted and passed in each stream.
Let the number of students admitted in the Arts stream be \( A \), in the IT stream be \( I \), and in the Science stream be \( S \).
- We know from the pie chart that the percentage of students in each stream is given.
- Let the total number of students admitted in all streams be \( T \), then:
- Arts = 10% of \( T \)
- IT = 10% of \( T \)
- Science = 35% of \( T \)
- Given that the number of students passing the examination in the Arts stream is 270 more than those passing in the IT stream and 50% of the students admitted in the Science stream passed the examination, we calculate that the total number of students admitted in all streams is 2400.
