Class 8 Ganita Prakash
Fractions in Disguise
Achievement Test - Part 9
Welcome to Part 9, the Grand Finale of the Chapter Achievement Test!
We conclude the Case Study Section (6 Marks Each) by tackling two enormous datasets involving 1000 and 1200 students respectively. You must carefully distinguish between fractions of the entire school and ratios of the remaining pool. Show your full working and cross-check against the official marking schemes in the solution tabs.
We conclude the Case Study Section (6 Marks Each) by tackling two enormous datasets involving 1000 and 1200 students respectively. You must carefully distinguish between fractions of the entire school and ratios of the remaining pool. Show your full working and cross-check against the official marking schemes in the solution tabs.
51 Excursion Transport Model C
Case Study Context:
A school is organizing a major educational excursion for its 1000 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: 6]
A school is organizing a major educational excursion for its 1000 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: 6]
(i) It is observed that \(\frac{1}{8}\) 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 \(3:1\). What percentage of these remaining students take the bus?
(iii) Additionally, if exactly 20% of the total 1000 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: 6]
(ii) The rest of the students take either a bus or a car in the ratio \(3:1\). What percentage of these remaining students take the bus?
(iii) Additionally, if exactly 20% of the total 1000 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: 6]
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 (\(3:1\)).
• Part (iii) requires finding an absolute number from a percentage.
• Part (iv) requires computing absolute numbers to make a comparison.[cite: 6]
• Part (i) asks for a simple fraction-to-percent conversion.
• Part (ii) requires finding a percentage from a ratio (\(3:1\)).
• Part (iii) requires finding an absolute number from a percentage.
• Part (iv) requires computing absolute numbers to make a comparison.[cite: 6]
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Hint:
1
For (ii): The ratio is 3 (bus) to 1 (car). Total parts = 4. Fraction for bus = \(\frac{3}{4}\). Convert this to a percentage.
2
For (iv): Find the absolute number of walkers. Since they are \(\frac{1}{8}\) of 1000, calculate \(1000 \div 8\). Then compare it to the answer from (iii).
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Mistakes to Avoid:
!
Calculating 75% of 1000: 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:
\(\frac{1}{8} \times 100\% = \frac{100}{8}\% = 12.5\%\).
(ii) Percentage of remaining taking the bus:
Ratio of bus to car is \(3:1\). Total parts = \(4\).
Fraction for bus = \(\frac{3}{4}\).
\(\frac{3}{4} \times 100\% = 3 \times 25\% = 75\%\).
(iii) Exact number using bicycles:
\(20\% \text{ of } 1000 = \frac{20}{100} \times 1000 = 200 \text{ students}\).
(iv) Comparison:
Number of walkers = \(\frac{1}{8} \text{ of } 1000 = 125 \text{ students}\).
Number of bicycles = \(200 \text{ students}\).
\(200 - 125 = 75\).
Ans: The bicycle group is larger by 75 students.
🎯 Marking Scheme (6 Marks Total):
• (i) 1 Mark for 12.5%.
• (ii) 2 Marks for calculating 75%.
• (iii) 1 Mark for 200 students.
• (iv) 2 Marks for calculating walkers (125) and stating the final difference (75).[cite: 6]
• (i) 1 Mark for 12.5%.
• (ii) 2 Marks for calculating 75%.
• (iii) 1 Mark for 200 students.
• (iv) 2 Marks for calculating walkers (125) and stating the final difference (75).[cite: 6]
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52 Excursion Transport Model D
Case Study Context:
A school is organizing a major educational excursion for its 1200 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: 8]
A school is organizing a major educational excursion for its 1200 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: 8]
(i) It is observed that \(\frac{3}{10}\) 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 \(4:1\). What percentage of these remaining students take the bus?
(iii) Additionally, if exactly 15% of the total 1200 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: 8]
(ii) The rest of the students take either a bus or a car in the ratio \(4:1\). What percentage of these remaining students take the bus?
(iii) Additionally, if exactly 15% of the total 1200 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: 8]
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 (\(4:1\)).
• Part (iii) requires finding an absolute number from a percentage.
• Part (iv) requires computing absolute numbers to make a comparison.[cite: 8]
• Part (i) asks for a simple fraction-to-percent conversion.
• Part (ii) requires finding a percentage from a ratio (\(4:1\)).
• Part (iii) requires finding an absolute number from a percentage.
• Part (iv) requires computing absolute numbers to make a comparison.[cite: 8]
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Hint:
1
For (ii): The ratio is 4 (bus) to 1 (car). Total parts = 5. Fraction for bus = \(\frac{4}{5}\). Convert this to a percentage.
2
For (iv): Find the absolute number of walkers. Since they are \(\frac{3}{10}\) of 1200, calculate \(\frac{3}{10} \times 1200\).
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Mistakes to Avoid:
!
Finding the smaller ratio part: In part (ii), the question explicitly asks for the percentage that takes the bus (which is the larger part of the 4:1 ratio). Do not calculate the percentage for the car (\(\frac{1}{5}\) = 20%).
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Solution:
(i) Percentage of walkers:
\(\frac{3}{10} \times 100\% = 3 \times 10\% = 30\%\).
(ii) Percentage of remaining taking the bus:
Ratio of bus to car is \(4:1\). Total parts = \(5\).
Fraction for bus = \(\frac{4}{5}\).
\(\frac{4}{5} \times 100\% = 4 \times 20\% = 80\%\).
(iii) Exact number using bicycles:
\(15\% \text{ of } 1200 = \frac{15}{100} \times 1200 = 15 \times 12 = 180 \text{ students}\).
(iv) Comparison:
Number of walkers = \(30\% \text{ of } 1200 = \frac{3}{10} \times 1200 = 360 \text{ students}\).
Number of bicycles = \(180 \text{ students}\).
\(360 - 180 = 180\).
Ans: The walking group is larger by 180 students.
🎯 Marking Scheme (6 Marks Total):
• (i) 1 Mark for 30%.
• (ii) 2 Marks for calculating 80%.
• (iii) 1 Mark for 180 students.
• (iv) 2 Marks for calculating walkers (360) and stating the final difference (180).[cite: 8]
• (i) 1 Mark for 30%.
• (ii) 2 Marks for calculating 80%.
• (iii) 1 Mark for 180 students.
• (iv) 2 Marks for calculating walkers (360) and stating the final difference (180).[cite: 8]
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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)
