Class 8 Ganita Prakash
Fractions in Disguise
Achievement Test - Part 8
Welcome to Part 8 of the Chapter Achievement Test! You have now entered the pinnacle of the exam: the Case Study Section (6 Marks Each).
In these advanced real-world scenarios, you must analyze a large dataset involving hundreds of students and multiple transport ratios. Pay close attention to whether a question asks for a percentage of the total group, or a percentage of the remaining group. Let's conquer the data!
In these advanced real-world scenarios, you must analyze a large dataset involving hundreds of students and multiple transport ratios. Pay close attention to whether a question asks for a percentage of the total group, or a percentage of the remaining group. Let's conquer the data!
49 Excursion Transport Model A
Case Study Context:
A school is organizing a major educational excursion for its 800 students. The students choose different modes of transport based on their location. You are tasked with analyzing the transport data provided by the administration.[cite: 2]
A school is organizing a major educational excursion for its 800 students. The students choose different modes of transport based on their location. You are tasked with analyzing the transport data provided by the administration.[cite: 2]
(i) It is observed that \(\frac{1}{5}\) of the total students walk to the destination. What percentage of the total students is this?
(ii) The rest of the students take either a bus or a car in the ratio \(3:2\). What percentage of these remaining students take the bus?
(iii) Additionally, if exactly 25% of the total 800 students use bicycles instead of any motor vehicle, calculate the exact number of students using bicycles.
(iv) Compare the number of students walking with the number of students using bicycles. Which group is larger, and by exactly how many students?[cite: 2]
(ii) The rest of the students take either a bus or a car in the ratio \(3:2\). What percentage of these remaining students take the bus?
(iii) Additionally, if exactly 25% of the total 800 students use bicycles instead of any motor vehicle, calculate the exact number of students using bicycles.
(iv) Compare the number of students walking with the number of students using bicycles. Which group is larger, and by exactly how many students?[cite: 2]
Concept:
1
A case study requires parsing multiple distinct data points.
• Part (i) asks for a simple fraction-to-percent conversion.
• Part (ii) requires finding a percentage from a ratio (\(3:2\)).
• Part (iii) requires finding an absolute number from a percentage.
• Part (iv) requires computing absolute numbers to make a comparison.[cite: 2]
• Part (i) asks for a simple fraction-to-percent conversion.
• Part (ii) requires finding a percentage from a ratio (\(3:2\)).
• Part (iii) requires finding an absolute number from a percentage.
• Part (iv) requires computing absolute numbers to make a comparison.[cite: 2]
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Hint:
1
For (ii): The ratio is 3 (bus) to 2 (car). Total parts = 5. Fraction for bus = \(\frac{3}{5}\). Convert this to a percentage.
2
For (iv): You must find the absolute number of walkers. Since they are \(\frac{1}{5}\) of 800, calculate \(800 \div 5\). Then compare it to the answer from (iii).
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Mistakes to Avoid:
!
Misreading part (ii): The question asks "What percentage of these remaining students take the bus?". It does NOT ask for the percentage of the total 800 students. Just convert the ratio \(3:2\) directly into a percentage (\(\frac{3}{5} \times 100\)).
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Solution:
(i) Percentage of walkers:
\(\frac{1}{5} \times 100\% = 20\%\).
(ii) Percentage of remaining taking the bus:
Ratio of bus to car is \(3:2\). Total parts = \(5\).
Fraction for bus = \(\frac{3}{5}\).
\(\frac{3}{5} \times 100\% = 3 \times 20\% = 60\%\).
(iii) Exact number using bicycles:
\(25\% \text{ of } 800 = \frac{1}{4} \times 800 = 200 \text{ students}\).
(iv) Comparison:
Number of walkers = \(20\% \text{ of } 800 = 160 \text{ students}\).
Number of bicycles = \(200 \text{ students}\).
\(200 - 160 = 40\).
Ans: The bicycle group is larger by 40 students.
🎯 Marking Scheme (6 Marks Total):
• (i) 1 Mark for 20%.
• (ii) 2 Marks for calculating 60%.
• (iii) 1 Mark for 200 students.
• (iv) 2 Marks for calculating walkers (160) and stating the final difference (40).[cite: 2]
• (i) 1 Mark for 20%.
• (ii) 2 Marks for calculating 60%.
• (iii) 1 Mark for 200 students.
• (iv) 2 Marks for calculating walkers (160) and stating the final difference (40).[cite: 2]
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50 Excursion Transport Model B
Case Study Context:
A school is organizing a major educational excursion for its 600 students. The students choose different modes of transport based on their location. You are tasked with analyzing the transport data provided by the administration.[cite: 4]
A school is organizing a major educational excursion for its 600 students. The students choose different modes of transport based on their location. You are tasked with analyzing the transport data provided by the administration.[cite: 4]
(i) It is observed that \(\frac{1}{4}\) of the total students walk to the destination. What percentage of the total students is this?
(ii) The rest of the students take either a bus or a car in the ratio \(7:3\). What percentage of these remaining students take the bus?
(iii) Additionally, if exactly 30% of the total 600 students use bicycles instead of any motor vehicle, calculate the exact number of students using bicycles.
(iv) Compare the number of students walking with the number of students using bicycles. Which group is larger, and by exactly how many students?[cite: 4]
(ii) The rest of the students take either a bus or a car in the ratio \(7:3\). What percentage of these remaining students take the bus?
(iii) Additionally, if exactly 30% of the total 600 students use bicycles instead of any motor vehicle, calculate the exact number of students using bicycles.
(iv) Compare the number of students walking with the number of students using bicycles. Which group is larger, and by exactly how many students?[cite: 4]
Concept:
1
A case study requires parsing multiple distinct data points.
• Part (i) asks for a simple fraction-to-percent conversion.
• Part (ii) requires finding a percentage from a ratio (\(7:3\)).
• Part (iii) requires finding an absolute number from a percentage.
• Part (iv) requires computing absolute numbers to make a comparison.[cite: 4]
• Part (i) asks for a simple fraction-to-percent conversion.
• Part (ii) requires finding a percentage from a ratio (\(7:3\)).
• Part (iii) requires finding an absolute number from a percentage.
• Part (iv) requires computing absolute numbers to make a comparison.[cite: 4]
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Hint:
1
For (ii): The ratio is 7 (bus) to 3 (car). Total parts = 10. Fraction for bus = \(\frac{7}{10}\).
2
For (iv): You must find the absolute number of walkers. Since they are \(\frac{1}{4}\) of 600, calculate \(600 \div 4\).
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Mistakes to Avoid:
!
Calculating 70% of 600: For part (ii), the question does NOT ask how many students took the bus out of the whole school. It asks for the percentage of the remaining group. Your final answer for (ii) is just a percentage!
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Solution:
(i) Percentage of walkers:
\(\frac{1}{4} \times 100\% = 25\%\).
(ii) Percentage of remaining taking the bus:
Ratio of bus to car is \(7:3\). Total parts = \(10\).
Fraction for bus = \(\frac{7}{10}\).
\(\frac{7}{10} \times 100\% = 7 \times 10\% = 70\%\).
(iii) Exact number using bicycles:
\(30\% \text{ of } 600 = \frac{30}{100} \times 600 = 30 \times 6 = 180 \text{ students}\).
(iv) Comparison:
Number of walkers = \(25\% \text{ of } 600 = \frac{1}{4} \times 600 = 150 \text{ students}\).
Number of bicycles = \(180 \text{ students}\).
\(180 - 150 = 30\).
Ans: The bicycle group is larger by 30 students.
🎯 Marking Scheme (6 Marks Total):
• (i) 1 Mark for 25%.
• (ii) 2 Marks for calculating 70%.
• (iii) 1 Mark for 180 students.
• (iv) 2 Marks for calculating walkers (150) and stating the final difference (30).[cite: 4]
• (i) 1 Mark for 25%.
• (ii) 2 Marks for calculating 70%.
• (iii) 1 Mark for 180 students.
• (iv) 2 Marks for calculating walkers (150) and stating the final difference (30).[cite: 4]
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Chapter Achievement Test 1.1
Part 1: Objective Mastery I
Q1 - Q10 (1 Mark Each)
Part 2: Objective Mastery II
Q11 - Q20 (1 Mark Each)
Part 3: Foundational Skills I
Q21 - Q26 (2 Marks Each)
Part 4: Foundational Skills II
Q27 - Q32 (2 Marks Each)
Part 5: Applied Problem Solving I
Q33 - Q38 (3 Marks Each)
Part 6: Applied Problem Solving II
Q39 - Q44 (3 Marks Each)
Part 7: Advanced Analysis
Q45 - Q48 (4 Marks Each)
Part 8: Real-World Applications I
Q49 - Q50 (6 Marks Each)
Part 9: Real-World Applications II
Q51 - Q52 (6 Marks Each)
