Class 8 Ganita Prakash
Fractions in Disguise
Achievement Test - Part 6
Welcome to Part 6 of the Chapter Achievement Test! We are wrapping up the Short Answer Section (3 Marks Each) with questions 39 through 44.
In this module, you must carefully compare absolute quantities derived from percentages (to see who consumed more sugar) and calculate exact numerical thresholds for achieving specific letter grades. Every solution features our interactive 4-pillar breakdown and the official marking scheme!
In this module, you must carefully compare absolute quantities derived from percentages (to see who consumed more sugar) and calculate exact numerical thresholds for achieving specific letter grades. Every solution features our interactive 4-pillar breakdown and the official marking scheme!
39 Comparative Sugar Analysis III
Sameer ate 140 g of a pudding having 25% sugar content. Riya ate 130 g of a different pudding having 30% sugar content. Calculate the exact grams of sugar consumed by each individual and state clearly who consumed more sugar.[cite: 5]
Concept:
1
To find the absolute amount of a component from a given weight and percentage, multiply the weight by the percentage decimal or fraction: \(\text{Weight} \times \frac{P}{100}\).[cite: 5]
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Hint:
1
Sameer's sugar = \(140 \times \frac{1}{4}\) (since 25% is a quarter).
2
Riya's sugar = \(130 \times \frac{30}{100} = 13 \times 3\).
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Mistakes to Avoid:
!
Comparing percentages directly: Do not assume Riya ate more just because 30% > 25%. You must calculate the actual grams before making a conclusion!
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Solution:
1. Sameer's sugar consumption:
\(140\text{ g} \times 25\% = 140 \times \frac{1}{4} = 35\text{ g}\)
2. Riya's sugar consumption:
\(130\text{ g} \times 30\% = 130 \times \frac{30}{100} = 13 \times 3 = 39\text{ g}\)
3. Comparison:
\(39\text{ g} > 35\text{ g}\), so Riya consumed more sugar.
Ans: Sameer: 35g, Riya: 39g; Riya consumed more.
🎯 Marking Scheme:
• 1 Mark for calculating Sameer's sugar (35 g).
• 1 Mark for calculating Riya's sugar (39 g).
• 1 Mark for clearly stating who consumed more.[cite: 5]
• 1 Mark for calculating Sameer's sugar (35 g).
• 1 Mark for calculating Riya's sugar (39 g).
• 1 Mark for clearly stating who consumed more.[cite: 5]
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40 Comparative Sugar Analysis IV
Dev ate 200 g of yogurt having 12% sugar content. Tara ate 150 g of a different yogurt having 18% sugar content. Calculate the exact grams of sugar consumed by each individual and state clearly who consumed more sugar.[cite: 7]
Concept:
1
Multiply each person's consumed weight by their respective sugar percentage fraction: \(\text{Weight} \times \frac{P}{100}\).[cite: 7]
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Hint:
1
Dev's sugar = \(200 \times \frac{12}{100}\).
2
Tara's sugar = \(150 \times \frac{18}{100}\). Cancel out the zeros first!
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Mistakes to Avoid:
!
Decimal multiplication errors: When calculating Tara's sugar, \(15 \times 1.8 = 27\). Do not accidentally evaluate it as 2.7!
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Solution:
1. Dev's sugar consumption:
\(200\text{ g} \times 12\% = 200 \times \frac{12}{100} = 2 \times 12 = 24\text{ g}\)
2. Tara's sugar consumption:
\(150\text{ g} \times 18\% = 150 \times \frac{18}{100} = 15 \times 1.8 = 27\text{ g}\)
3. Comparison:
\(27\text{ g} > 24\text{ g}\), so Tara consumed more sugar.
Ans: Dev: 24g, Tara: 27g; Tara consumed more.
🎯 Marking Scheme:
• 1 Mark for calculating Dev's sugar (24 g).
• 1 Mark for calculating Tara's sugar (27 g).
• 1 Mark for stating who consumed more.[cite: 7]
• 1 Mark for calculating Dev's sugar (24 g).
• 1 Mark for calculating Tara's sugar (27 g).
• 1 Mark for stating who consumed more.[cite: 7]
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41 Grade Threshold Calculation I
A student needs to score 75% or above on an 80-mark test to get an A+ grade. Calculate the exact minimum marks required to achieve this grade, showing your steps clearly.[cite: 1]
Concept:
1
To find a specific percentage of a total, multiply the total marks by the percentage fraction: \(\text{Total} \times \frac{P}{100}\).[cite: 1]
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Hint:
1
75% is a very common fraction. It is exactly \(\frac{3}{4}\).
2
Calculate \(\frac{3}{4} \times 80\).
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Mistakes to Avoid:
!
Finding 25% and forgetting to subtract: If you calculate \(\frac{1}{4}\) of 80 (which is 20) but forget to subtract it from 80, your answer will be completely wrong!
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Solution:
Total marks = \(80\)
Required percentage = \(75\%\)
\(\text{Minimum marks} = 75\% \text{ of } 80\)
\(= \frac{75}{100} \times 80\)
\(= \frac{3}{4} \times 80\)
\(= 3 \times 20 = 60\)
Ans: The minimum required marks is 60.
🎯 Marking Scheme:
• 1 Mark for setting up the equation (75/100 × 80).
• 1 Mark for correct calculation steps (e.g., 3/4 × 80).
• 1 Mark for the correct final answer (60 marks).[cite: 1]
• 1 Mark for setting up the equation (75/100 × 80).
• 1 Mark for correct calculation steps (e.g., 3/4 × 80).
• 1 Mark for the correct final answer (60 marks).[cite: 1]
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42 Grade Threshold Calculation II
A student needs to score 85% or above on a 60-mark test to get an A+ grade. Calculate the exact minimum marks required to achieve this grade, showing your steps clearly.[cite: 3]
Concept:
1
Calculate \(85\%\) of \(60\) by simplifying the percentage fraction first: \(\frac{85}{100} = \frac{17}{20}\).[cite: 3]
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Hint:
1
Multiply \(\frac{17}{20}\) by \(60\).
2
What is \(60 \div 20\)? It's exactly 3. Now multiply 17 by 3.
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Mistakes to Avoid:
!
Heavy Multiplication: Do not calculate \(85 \times 60 = 5100\) and then divide by 100 if you don't have to. Simplifying fractions first prevents arithmetic errors!
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Solution:
Total marks = \(60\)
Required percentage = \(85\%\)
\(\text{Minimum marks} = 85\% \text{ of } 60\)
\(= \frac{85}{100} \times 60\)
\(= \frac{17}{20} \times 60\)
\(= 17 \times 3 = 51\)
Ans: The minimum required marks is 51.
🎯 Marking Scheme:
• 1 Mark for setting up the equation (85/100 × 60).
• 1 Mark for correct calculation steps (e.g., 17/20 × 60).
• 1 Mark for the correct final answer (51 marks).[cite: 3]
• 1 Mark for setting up the equation (85/100 × 60).
• 1 Mark for correct calculation steps (e.g., 17/20 × 60).
• 1 Mark for the correct final answer (51 marks).[cite: 3]
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43 Grade Threshold Calculation III
A student needs to score 70% or above on a 90-mark test to get an A+ grade. Calculate the exact minimum marks required to achieve this grade, showing your steps clearly.[cite: 5]
Concept:
1
Calculate \(70\%\) of \(90\). Since both numbers end in zero, you can mentally find 10% and multiply by 7.[cite: 5]
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Hint:
1
\(10\%\) of \(90\) is \(9\).
2
Multiply by 7: \(9 \times 7 = ?\)
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Mistakes to Avoid:
!
Adding instead of multiplying: Do not calculate \(9+7 = 16\). Scaling percentages requires multiplication!
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Solution:
Total marks = \(90\)
Required percentage = \(70\%\)
\(\text{Minimum marks} = 70\% \text{ of } 90\)
\(= \frac{70}{100} \times 90\)
\(= 7 \times 9 = 63\)
Ans: The minimum required marks is 63.
🎯 Marking Scheme:
• 1 Mark for setting up the equation (70/100 × 90).
• 1 Mark for correct calculation steps.
• 1 Mark for the correct final answer (63 marks).[cite: 5]
• 1 Mark for setting up the equation (70/100 × 90).
• 1 Mark for correct calculation steps.
• 1 Mark for the correct final answer (63 marks).[cite: 5]
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44 Grade Threshold Calculation IV
A student needs to score 90% or above on a 50-mark test to get an A+ grade. Calculate the exact minimum marks required to achieve this grade, showing your steps clearly.[cite: 7]
Concept:
1
You can find \(90\%\) by calculating \(100\%\) minus \(10\%\). It's a powerful mental math trick![cite: 7]
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Hint:
1
\(10\%\) of \(50\) is \(5\).
2
Subtract \(5\) from the total marks (\(50\)).
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Mistakes to Avoid:
!
Finding 10% and stopping: A common error is writing down "5" as the final answer. 5 marks would be an F, not an A+! You must subtract it from 50.
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Solution:
Total marks = \(50\)
Required percentage = \(90\%\)
Method 1 (Standard):
\(\text{Minimum marks} = \frac{90}{100} \times 50\)
\(= 9 \times 5 = 45\)
Method 2 (Mental Math):
\(10\% \text{ of } 50 = 5\)
\(90\% = 50 - 5 = 45\)
Ans: The minimum required marks is 45.
🎯 Marking Scheme:
• 1 Mark for setting up the equation (90/100 × 50) or mental logic.
• 1 Mark for correct calculation steps.
• 1 Mark for the correct final answer (45 marks).[cite: 7]
• 1 Mark for setting up the equation (90/100 × 50) or mental logic.
• 1 Mark for correct calculation steps.
• 1 Mark for the correct final answer (45 marks).[cite: 7]
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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)
