Class 8 Ganita Prakash
Fractions in Disguise
Achievement Test - Part 7
Welcome to Part 7 of the Chapter Achievement Test! You have now entered the Long Answer Section (4 Marks Each).
In these advanced questions (Q45 to Q48), you will solve complex, multi-step journey word problems. You must calculate the total distance from a given percentage, find the remaining distance, and translate your findings into a rough visual proportional bar model. Let's conquer these logic puzzles!
In these advanced questions (Q45 to Q48), you will solve complex, multi-step journey word problems. You must calculate the total distance from a given percentage, find the remaining distance, and translate your findings into a rough visual proportional bar model. Let's conquer these logic puzzles!
45 Journey Proportions I
A driver travels from Mumbai to Pune. He completes 45% of his journey, which covers exactly 81 km. Find the total distance of the journey between the two cities. Also, calculate the remaining distance he has to travel, and draw a rough proportional bar model to represent this situation.[cite: 2]
Concept:
1
This is a 3-part problem. First, find the total distance (\(D\)) using the equation: \(45\% \times D = 81\).[cite: 2]
2
Second, find the remaining distance by subtracting the covered distance from the total.
3
Third, visually represent these two parts on a 100% scale bar model.
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Hint:
1
\(\text{Total Distance} = 81 \times \frac{100}{45}\).
2
Both 81 and 45 are multiples of 9! Simplify the fraction.
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Mistakes to Avoid:
!
Finding 45% of 81: Do not multiply 81 by 0.45. The text explicitly states that 45% *IS* the 81 km. You must divide to find the total whole.
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Solution:
1. Total Distance:
Let total distance be \(D\).
\(45\% \text{ of } D = 81\)
\(\frac{45}{100} \times D = 81 \implies D = 81 \times \frac{100}{45}\)
Divide 81 and 45 by 9: \(D = 9 \times \frac{100}{5} = 9 \times 20 = 180 \text{ km}\).
2. Remaining Distance:
\(\text{Remaining} = 180 - 81 = 99 \text{ km}\) (This is 55% of the journey).
3. Proportional Bar Model:
Covered: 45%
(81 km)
(81 km)
Remaining: 55%
(99 km)
(99 km)
🎯 Marking Scheme:
• 2 Marks for calculating total distance (180 km).
• 1 Mark for calculating remaining distance (99 km).
• 1 Mark for drawing a labeled bar model.[cite: 2]
• 2 Marks for calculating total distance (180 km).
• 1 Mark for calculating remaining distance (99 km).
• 1 Mark for drawing a labeled bar model.[cite: 2]
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46 Journey Proportions II
A driver travels from Chennai to Vellore. He completes 35% of his journey, which covers exactly 49 km. Find the total distance of the journey between the two cities. Also, calculate the remaining distance he has to travel, and draw a rough proportional bar model to represent this situation.[cite: 4]
Concept:
1
Calculate the full distance by isolating the variable \(D\): \(D = 49 \div \frac{35}{100}\).[cite: 4]
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Hint:
1
\(D = 49 \times \frac{100}{35}\). Notice that 49 and 35 are both multiples of 7!
2
Subtract 49 from your total to get the remaining distance.
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Mistakes to Avoid:
!
Bar model scaling: Since 35% is covered, the "Remaining" section (65%) should be visibly wider than the "Covered" section in your diagram.
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Solution:
1. Total Distance:
Let total distance be \(D\).
\(\frac{35}{100} \times D = 49 \implies D = 49 \times \frac{100}{35}\)
Divide 49 and 35 by 7: \(D = 7 \times \frac{100}{5} = 7 \times 20 = 140 \text{ km}\).
2. Remaining Distance:
\(\text{Remaining} = 140 - 49 = 91 \text{ km}\) (This is 65% of the journey).
3. Proportional Bar Model:
Covered: 35%
(49 km)
(49 km)
Remaining: 65%
(91 km)
(91 km)
🎯 Marking Scheme:
• 2 Marks for total distance (140 km).
• 1 Mark for remaining distance (91 km).
• 1 Mark for labeled bar model.[cite: 4]
• 2 Marks for total distance (140 km).
• 1 Mark for remaining distance (91 km).
• 1 Mark for labeled bar model.[cite: 4]
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47 Journey Proportions III
A driver travels from Jaipur to Ajmer. He completes 55% of his journey, which covers exactly 77 km. Find the total distance of the journey between the two cities. Also, calculate the remaining distance he has to travel, and draw a rough proportional bar model to represent this situation.[cite: 6]
Concept:
1
Calculate the full distance: \(D = 77 \div \frac{55}{100}\).[cite: 6]
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Hint:
1
\(D = 77 \times \frac{100}{55}\). Both 77 and 55 divide cleanly by 11.
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Mistakes to Avoid:
!
Bar model scaling: Since 55% is covered, the "Covered" section should be slightly larger than the "Remaining" section (45%).
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Solution:
1. Total Distance:
Let total distance be \(D\).
\(\frac{55}{100} \times D = 77 \implies D = 77 \times \frac{100}{55}\)
Divide 77 and 55 by 11: \(D = 7 \times \frac{100}{5} = 7 \times 20 = 140 \text{ km}\).
2. Remaining Distance:
\(\text{Remaining} = 140 - 77 = 63 \text{ km}\) (This is 45% of the journey).
3. Proportional Bar Model:
Covered: 55%
(77 km)
(77 km)
Remaining: 45%
(63 km)
(63 km)
🎯 Marking Scheme:
• 2 Marks for total distance (140 km).
• 1 Mark for remaining distance (63 km).
• 1 Mark for labeled bar model.[cite: 6]
• 2 Marks for total distance (140 km).
• 1 Mark for remaining distance (63 km).
• 1 Mark for labeled bar model.[cite: 6]
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48 Journey Proportions IV
A driver travels from Kochi to Munnar. He completes 65% of his journey, which covers exactly 91 km. Find the total distance of the journey between the two cities. Also, calculate the remaining distance he has to travel, and draw a rough proportional bar model to represent this situation.[cite: 8]
Concept:
1
Calculate the full distance: \(D = 91 \div \frac{65}{100}\).[cite: 8]
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Hint:
1
\(D = 91 \times \frac{100}{65}\). Both 91 and 65 divide cleanly by 13.
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Mistakes to Avoid:
!
Bar model scaling: Since 65% is covered, the "Covered" section should be notably larger (almost double) the "Remaining" section (35%).
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Solution:
1. Total Distance:
Let total distance be \(D\).
\(\frac{65}{100} \times D = 91 \implies D = 91 \times \frac{100}{65}\)
Divide 91 and 65 by 13: \(D = 7 \times \frac{100}{5} = 7 \times 20 = 140 \text{ km}\).
2. Remaining Distance:
\(\text{Remaining} = 140 - 91 = 49 \text{ km}\) (This is 35% of the journey).
3. Proportional Bar Model:
Covered: 65%
(91 km)
(91 km)
Remaining: 35%
(49 km)
(49 km)
🎯 Marking Scheme:
• 2 Marks for total distance (140 km).
• 1 Mark for remaining distance (49 km).
• 1 Mark for labeled bar model.[cite: 8]
• 2 Marks for total distance (140 km).
• 1 Mark for remaining distance (49 km).
• 1 Mark for labeled bar model.[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)
