Class 8 Ganita Prakash
Fractions in Disguise
Achievement Test - Part 5
Welcome to Part 5 of the Chapter Achievement Test! We now enter the Short Answer Section (3 Marks Each), covering questions 33 through 38.
These questions test your ability to work with ratio mixtures (such as mango drinks, orange squashes, and lemonades), convert those ratios into percentages, and scale them to find exact component volumes. Every solution includes complete step-by-step working and the official 3-mark scoring scheme!
These questions test your ability to work with ratio mixtures (such as mango drinks, orange squashes, and lemonades), convert those ratios into percentages, and scale them to find exact component volumes. Every solution includes complete step-by-step working and the official 3-mark scoring scheme!
33 Ratio & Percentage Mixtures I
In a mango drink, the ratio of mango pulp to water is 2:3. What percentage of the entire drink is mango pulp? If you prepare 600 ml of this drink, exactly how many ml of mango pulp are used?[cite: 2]
Concept:
1
To find a component's percentage from a ratio (\(A:B\)), first add the parts to find the total parts (\(A + B\)). Then express part \(A\) as a fraction over the total: \(\frac{A}{A+B}\).[cite: 2]
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Hint:
1
Total parts = \(2 + 3 = 5\). Mango pulp fraction = \(\frac{2}{5}\).
2
Percentage = \(\frac{2}{5} \times 100\%\). Volume = \(\frac{2}{5} \times 600\text{ ml}\).
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Mistakes to Avoid:
!
Using water as the denominator: Do not write \(\frac{2}{3}\). The total parts in the mixture include both pulp and water (\(2+3=5\)).
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Solution:
1. Find total parts in ratio \(2:3\):
\(\text{Total parts} = 2 + 3 = 5\)
2. Calculate percentage of mango pulp:
\(\text{Percentage} = \frac{2}{5} \times 100\% = 2 \times 20\% = 40\%\)
3. Calculate exact ml of mango pulp in 600 ml:
\(\text{Volume} = \frac{2}{5} \times 600\text{ ml} = 2 \times 120\text{ ml} = 240\text{ ml}\)
Ans: 40% pulp; Exactly 240 ml used.
🎯 Marking Scheme:
• 1 Mark for calculating total parts (5) and the fraction (2/5).
• 1 Mark for calculating the correct percentage (40%).
• 1 Mark for calculating the correct volume in ml (240 ml).[cite: 2]
• 1 Mark for calculating total parts (5) and the fraction (2/5).
• 1 Mark for calculating the correct percentage (40%).
• 1 Mark for calculating the correct volume in ml (240 ml).[cite: 2]
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34 Ratio & Percentage Mixtures II
In an orange squash, the ratio of syrup to water is 1:4. What percentage of the entire squash is syrup? If you prepare 500 ml of this squash, exactly how many ml of syrup are used?[cite: 4]
Concept:
1
Total parts = \(1 + 4 = 5\). Syrup fraction = \(\frac{1}{5}\).[cite: 4]
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Hint:
1
Percentage = \(\frac{1}{5} \times 100\%\). Volume = \(\frac{1}{5} \times 500\text{ ml}\).
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Mistakes to Avoid:
!
Using 4 as the denominator: Water is 4 parts, but the total mixture is 5 parts.
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Solution:
1. Find total parts in ratio \(1:4\):
\(\text{Total parts} = 1 + 4 = 5\)
2. Calculate percentage of syrup:
\(\text{Percentage} = \frac{1}{5} \times 100\% = 20\%\)
3. Calculate exact ml of syrup in 500 ml:
\(\text{Volume} = \frac{1}{5} \times 500\text{ ml} = 100\text{ ml}\)
Ans: 20% syrup; Exactly 100 ml used.
🎯 Marking Scheme:
• 1 Mark for total parts (5) and fraction (1/5).
• 1 Mark for percentage (20%).
• 1 Mark for volume (100 ml).[cite: 4]
• 1 Mark for total parts (5) and fraction (1/5).
• 1 Mark for percentage (20%).
• 1 Mark for volume (100 ml).[cite: 4]
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35 Ratio & Percentage Mixtures III
In fresh lemonade, the ratio of lemon juice to water is 1:3. What percentage of the entire drink is lemon juice? If you prepare 800 ml of this drink, exactly how many ml of lemon juice are used?[cite: 6]
Concept:
1
Total parts = \(1 + 3 = 4\). Lemon juice fraction = \(\frac{1}{4}\) (which is 25%).[cite: 6]
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Hint:
1
Percentage = \(\frac{1}{4} \times 100\%\). Volume = \(\frac{1}{4} \times 800\text{ ml}\).
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Mistakes to Avoid:
!
Using 3 as the denominator: Water is 3 parts, but the entire drink is 4 parts.
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Solution:
1. Find total parts in ratio \(1:3\):
\(\text{Total parts} = 1 + 3 = 4\)
2. Calculate percentage of lemon juice:
\(\text{Percentage} = \frac{1}{4} \times 100\% = 25\%\)
3. Calculate exact ml of lemon juice in 800 ml:
\(\text{Volume} = \frac{1}{4} \times 800\text{ ml} = 200\text{ ml}\)
Ans: 25% lemon juice; Exactly 200 ml used.
🎯 Marking Scheme:
• 1 Mark for total parts (4) and fraction (1/4).
• 1 Mark for percentage (25%).
• 1 Mark for volume (200 ml).[cite: 6]
• 1 Mark for total parts (4) and fraction (1/4).
• 1 Mark for percentage (25%).
• 1 Mark for volume (200 ml).[cite: 6]
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36 Ratio & Percentage Mixtures IV
In a rose milk drink, the ratio of rose syrup to milk is 1:9. What percentage of the entire drink is rose syrup? If you prepare 1000 ml of this drink, exactly how many ml of rose syrup are used?[cite: 8]
Concept:
1
Total parts = \(1 + 9 = 10\). Rose syrup fraction = \(\frac{1}{10}\) (which is 10%).[cite: 8]
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Hint:
1
Percentage = \(\frac{1}{10} \times 100\%\). Volume = \(\frac{1}{10} \times 1000\text{ ml}\).
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Mistakes to Avoid:
!
Using 9 as the denominator: Milk is 9 parts, but the entire drink is 10 parts.
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Solution:
1. Find total parts in ratio \(1:9\):
\(\text{Total parts} = 1 + 9 = 10\)
2. Calculate percentage of rose syrup:
\(\text{Percentage} = \frac{1}{10} \times 100\% = 10\%\)
3. Calculate exact ml of rose syrup in 1000 ml:
\(\text{Volume} = \frac{1}{10} \times 1000\text{ ml} = 100\text{ ml}\)
Ans: 10% rose syrup; Exactly 100 ml used.
🎯 Marking Scheme:
• 1 Mark for total parts (10) and fraction (1/10).
• 1 Mark for percentage (10%).
• 1 Mark for volume (100 ml).[cite: 8]
• 1 Mark for total parts (10) and fraction (1/10).
• 1 Mark for percentage (10%).
• 1 Mark for volume (100 ml).[cite: 8]
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37 Comparative Sugar Analysis I
Priya ate 150 g of a cake having 20% sugar content. Rahul ate 120 g of a different cake having 30% sugar content. Calculate the exact grams of sugar consumed by each individual and state clearly who consumed more sugar.[cite: 2]
Concept:
1
To find the absolute amount of a component from a given weight and percentage, multiply weight by the percentage decimal: \(\text{Weight} \times \frac{P}{100}\).[cite: 2]
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Hint:
1
Priya's sugar = \(150 \times 0.20\). Rahul's sugar = \(120 \times 0.30\).
2
Compare the two resulting gram amounts.
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Mistakes to Avoid:
!
Comparing percentages directly: Do not assume Rahul ate more just because 30% is greater than 20%. You must calculate the absolute mass in grams.
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Solution:
1. Priya's sugar consumption:
\(150\text{ g} \times 20\% = 150 \times 0.20 = 30\text{ g}\)
2. Rahul's sugar consumption:
\(120\text{ g} \times 30\% = 120 \times 0.30 = 36\text{ g}\)
3. Comparison:
\(36\text{ g} > 30\text{ g}\), so Rahul consumed more sugar.
Ans: Priya: 30g, Rahul: 36g; Rahul consumed more.
🎯 Marking Scheme:
• 1 Mark for calculating Priya's sugar (30 g).
• 1 Mark for calculating Rahul's sugar (36 g).
• 1 Mark for clearly stating who consumed more.[cite: 2]
• 1 Mark for calculating Priya's sugar (30 g).
• 1 Mark for calculating Rahul's sugar (36 g).
• 1 Mark for clearly stating who consumed more.[cite: 2]
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38 Comparative Sugar Analysis II
Kabir ate 160 g of a pie having 15% sugar content. Zara ate 110 g of a different pie having 20% sugar content. Calculate the exact grams of sugar consumed by each individual and state clearly who consumed more sugar.[cite: 4]
Concept:
1
Multiply each person's consumed weight by their respective sugar percentage decimal.[cite: 4]
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Hint:
1
Kabir's sugar = \(160 \times 0.15\). Zara's sugar = \(110 \times 0.20\).
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Mistakes to Avoid:
!
Comparing percentages directly: Do not rely on 20% being greater than 15%. Weight matters!
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Solution:
1. Kabir's sugar consumption:
\(160\text{ g} \times 15\% = 160 \times 0.15 = 24\text{ g}\)
2. Zara's sugar consumption:
\(110\text{ g} \times 20\% = 110 \times 0.20 = 22\text{ g}\)
3. Comparison:
\(24\text{ g} > 22\text{ g}\), so Kabir consumed more sugar.
Ans: Kabir: 24g, Zara: 22g; Kabir consumed more.
🎯 Marking Scheme:
• 1 Mark for Kabir's sugar (24 g).
• 1 Mark for Zara's sugar (22 g).
• 1 Mark for stating who consumed more.[cite: 4]
• 1 Mark for Kabir's sugar (24 g).
• 1 Mark for Zara's sugar (22 g).
• 1 Mark for stating who consumed more.[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)
