Chapter 9 of 15
Chapter 9: Coconut Farm
नारियल का बाग (गुणन व्यूह, गुणनखंड वृक्ष एवं विभाजन) | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Rectangular arrays: Visualizing multiplication as Rows × Columns.
- Box/Grid Multiplication Method: Breaking two-digit numbers by expanded form.
- Factor Trees: Finding prime factorizations and factor pairs of composite numbers.
- Division with remainder: Dividend = Divisor × Quotient + Remainder.
- (a) Number of faces: An open box without a top lid has 1 base + 4 side walls = 5 square faces.
- (b) Area of 1 face: $5\text{ cm} \times 5\text{ cm} = 25\text{ cm}^2$.
- Total surface area: $5 \times 25\text{ cm}^2 = \mathbf{125\text{ cm}^2}$.
All Textbook Exercises & In-Text Tasks (24 Questions)
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Q1
Coconut Orchard Planting • Multiplication Grid
A coconut grove has 24 rows of trees, with 18 trees in each row.
(a) Find the total number of coconut trees in the orchard using the box/grid multiplication method.
(b) Verify using the standard column multiplication algorithm.
[3 Marks]
(a) Find the total number of coconut trees in the orchard using the box/grid multiplication method.
(b) Verify using the standard column multiplication algorithm.
✅ Step-by-Step Solution & Working
Multiplication Working (24 × 18):
• (a) Box Method: Split 24 into 20 + 4, and 18 into 10 + 8:
- 20 × 10 = 200
- 4 × 10 = 40
- 20 × 8 = 160
- 4 × 8 = 32
- Sum = 200 + 40 + 160 + 32 = 432 trees.
• (b) Column Method: 24 × 8 = 192; 24 × 10 = 240; 192 + 240 = 432 trees. Both methods match!
• (a) Box Method: Split 24 into 20 + 4, and 18 into 10 + 8:
- 20 × 10 = 200
- 4 × 10 = 40
- 20 × 8 = 160
- 4 × 8 = 32
- Sum = 200 + 40 + 160 + 32 = 432 trees.
• (b) Column Method: 24 × 8 = 192; 24 × 10 = 240; 192 + 240 = 432 trees. Both methods match!
CBSE Step-by-Step Marking Scheme
Box method working
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Column verification = 432 trees
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Q2
Harvest Yield • Coconut Packing in Sacks
A farmer plucks 2,160 coconuts. He packs them into sacks of 45 coconuts each.
(a) How many full sacks are packed?
(b) If each sack is sold for ₹1,125, what is his total earnings from selling all the sacks?
[3 Marks]
(a) How many full sacks are packed?
(b) If each sack is sold for ₹1,125, what is his total earnings from selling all the sacks?
✅ Step-by-Step Solution & Working
Working:
• (a) Sacks Packed: 2,160 ÷ 45 = 48 sacks.
• (b) Total Earnings: 48 sacks × ₹1,125 = ₹54,000.
• (a) Sacks Packed: 2,160 ÷ 45 = 48 sacks.
• (b) Total Earnings: 48 sacks × ₹1,125 = ₹54,000.
CBSE Step-by-Step Marking Scheme
Sacks packed = 48
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Total revenue = ₹54,000
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Q3
Coconut Water Stalls • Daily Earnings
A roadside tender coconut vendor buys coconuts from the farm at ₹28 each and sells fresh coconut water at ₹45 each.
(a) What is his profit on 1 coconut?
(b) If he sells 65 coconuts on Sunday, calculate his total sales revenue and net profit.
[3 Marks]
(a) What is his profit on 1 coconut?
(b) If he sells 65 coconuts on Sunday, calculate his total sales revenue and net profit.
✅ Step-by-Step Solution & Working
Profit & Revenue Calculations:
• (a) Profit per Coconut: ₹45 - ₹28 = ₹17 profit per coconut.
• (b) Sunday Sales (65 Coconuts):
- Total revenue = 65 × ₹45 = ₹2,925.
- Cost price = 65 × ₹28 = ₹1,820.
- Net profit = 65 × ₹17 = ₹1,105.
• (a) Profit per Coconut: ₹45 - ₹28 = ₹17 profit per coconut.
• (b) Sunday Sales (65 Coconuts):
- Total revenue = 65 × ₹45 = ₹2,925.
- Cost price = 65 × ₹28 = ₹1,820.
- Net profit = 65 × ₹17 = ₹1,105.
CBSE Step-by-Step Marking Scheme
Profit per coconut = ₹17
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Total revenue = ₹2,925
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Net profit = ₹1,105
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Q4
Sapling Nursery • Planting in Beds
A school gardener receives 576 plant saplings. He wants to plant them in 18 equal rows.
(a) How many saplings will be planted in each row?
(b) If he had 600 saplings instead, how many saplings would be in each row and how many would be left over?
[3 Marks]
(a) How many saplings will be planted in each row?
(b) If he had 600 saplings instead, how many saplings would be in each row and how many would be left over?
✅ Step-by-Step Solution & Working
Division with and without Remainder:
• (a) 576 Saplings in 18 Rows: 576 ÷ 18 = 32 saplings per row.
• (b) 600 Saplings in 18 Rows:
- 600 ÷ 18 gives quotient 33 with remainder 6 (18 × 33 = 594; 600 - 594 = 6).
- 33 saplings per row with 6 saplings left over.
• (a) 576 Saplings in 18 Rows: 576 ÷ 18 = 32 saplings per row.
• (b) 600 Saplings in 18 Rows:
- 600 ÷ 18 gives quotient 33 with remainder 6 (18 × 33 = 594; 600 - 594 = 6).
- 33 saplings per row with 6 saplings left over.
CBSE Step-by-Step Marking Scheme
576 ÷ 18 = 32 saplings
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600 ÷ 18 = 33 per row with remainder 6
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Q5
Coconut Oil Mill • Extraction Proportions
A copra oil mill extracts 1 litre of pure coconut oil from every 15 dry coconuts.
(a) How many litres of oil are produced from 1,800 coconuts?
(b) If 1 litre of coconut oil sells for ₹240, what is the value of the oil produced?
[3 Marks]
(a) How many litres of oil are produced from 1,800 coconuts?
(b) If 1 litre of coconut oil sells for ₹240, what is the value of the oil produced?
✅ Step-by-Step Solution & Working
Proportion Calculations:
• (a) Oil Extracted: 1,800 ÷ 15 = 120 litres of oil.
• (b) Market Value: 120 L × ₹240 = ₹28,800.
• (a) Oil Extracted: 1,800 ÷ 15 = 120 litres of oil.
• (b) Market Value: 120 L × ₹240 = ₹28,800.
CBSE Step-by-Step Marking Scheme
Oil produced = 120 L
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Market value = ₹28,800
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Q6
Multi-digit Multiplication • Distributive Property
Evaluate using the distributive property: $48 \times 25$. Show how you can compute this quickly by thinking of 25 as 100 ÷ 4.
[3 Marks]
✅ Step-by-Step Solution & Working
Mental Arithmetic Strategies:
• Method 1 (Distributive): 48 × (20 + 5) = (48 × 20) + (48 × 5) = 960 + 240 = 1,200.
• Method 2 (Quarter of 100): 25 = 100 ÷ 4.
48 × 25 = (48 × 100) ÷ 4 = 4,800 ÷ 4 = 1,200.
• Method 1 (Distributive): 48 × (20 + 5) = (48 × 20) + (48 × 5) = 960 + 240 = 1,200.
• Method 2 (Quarter of 100): 25 = 100 ÷ 4.
48 × 25 = (48 × 100) ÷ 4 = 4,800 ÷ 4 = 1,200.
CBSE Step-by-Step Marking Scheme
Distributive method steps
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Quarter-hundred method = 1,200
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Q7
Worker Wages • Daily and Weekly Share
A coconut grove employs 8 workers for harvesting. The owner pays each worker ₹450 per day.
(a) What is the total wage bill for all 8 workers for one day?
(b) If the harvest work lasts for 6 days, what is the total amount paid in wages?
[3 Marks]
(a) What is the total wage bill for all 8 workers for one day?
(b) If the harvest work lasts for 6 days, what is the total amount paid in wages?
✅ Step-by-Step Solution & Working
Wage Calculations:
• (a) Daily Total for 8 Workers: 8 × ₹450 = ₹3,600 per day.
• (b) 6-Day Wage Bill: 6 × ₹3,600 = ₹21,600.
• (a) Daily Total for 8 Workers: 8 × ₹450 = ₹3,600 per day.
• (b) 6-Day Wage Bill: 6 × ₹3,600 = ₹21,600.
CBSE Step-by-Step Marking Scheme
Daily wages = ₹3,600
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6-day wages = ₹21,600
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Q8
Truck Loading Capacity • Gross Weight
A small tempo truck can carry a maximum payload of 1,500 kg. A bag of 50 coconuts weighs 30 kg.
(a) What is the maximum number of such bags the truck can safely transport in one trip?
(b) How many total coconuts are transported in that full truck load?
[3 Marks]
(a) What is the maximum number of such bags the truck can safely transport in one trip?
(b) How many total coconuts are transported in that full truck load?
✅ Step-by-Step Solution & Working
Payload Calculations:
• (a) Maximum Bags: 1,500 kg ÷ 30 kg/bag = 50 bags.
• (b) Total Coconuts: 50 bags × 50 coconuts/bag = 2,500 coconuts.
• (a) Maximum Bags: 1,500 kg ÷ 30 kg/bag = 50 bags.
• (b) Total Coconuts: 50 bags × 50 coconuts/bag = 2,500 coconuts.
CBSE Step-by-Step Marking Scheme
Max bags = 50
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Total coconuts = 2,500
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Q9
Irrigation Drip System • Water Flow
An automated drip irrigation pipe delivers 2.5 litres of water per hour to each coconut tree. The grove has 160 trees and the pump runs for 4 hours daily.
(a) How many litres of water does one tree receive in 4 hours?
(b) How many litres of water are supplied to the entire grove daily?
[3 Marks]
(a) How many litres of water does one tree receive in 4 hours?
(b) How many litres of water are supplied to the entire grove daily?
✅ Step-by-Step Solution & Working
Water Delivery Calculations:
• (a) Water per Tree: 4 hours × 2.5 L/h = 10 litres per tree.
• (b) Total Daily Water for 160 Trees: 160 × 10 L = 1,600 litres.
• (a) Water per Tree: 4 hours × 2.5 L/h = 10 litres per tree.
• (b) Total Daily Water for 160 Trees: 160 × 10 L = 1,600 litres.
CBSE Step-by-Step Marking Scheme
One tree = 10 L
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Total grove = 1,600 L
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Q10
Division Verification Algorithm
Divide 1,485 by 12. State the quotient and the remainder, and verify your answer using the formula: $\text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}$.
[3 Marks]
✅ Step-by-Step Solution & Working
Division & Proof:
1. 1,485 ÷ 12:
• 12 × 100 = 1,200 (Remainder 285)
• 12 × 20 = 240 (Remainder 45)
• 12 × 3 = 36 (Remainder 9)
Quotient = 123, Remainder = 9.
2. Verification:
(12 × 123) + 9 = 1,476 + 9 = 1,485. The division is verified!
1. 1,485 ÷ 12:
• 12 × 100 = 1,200 (Remainder 285)
• 12 × 20 = 240 (Remainder 45)
• 12 × 3 = 36 (Remainder 9)
Quotient = 123, Remainder = 9.
2. Verification:
(12 × 123) + 9 = 1,476 + 9 = 1,485. The division is verified!
CBSE Step-by-Step Marking Scheme
Quotient = 123, Remainder = 9
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Verification formula step-by-step
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Q11
Coir Rope Production • Unitary Conversion
Coconut husks are processed into coir rope. From 100 coconut husks, 8 kg of coir fibre is obtained.
(a) How many kilograms of coir fibre can be made from 1,500 husks?
(b) If 1 kg of coir fibre makes 15 metres of rope, how many metres of rope can be produced?
[3 Marks]
(a) How many kilograms of coir fibre can be made from 1,500 husks?
(b) If 1 kg of coir fibre makes 15 metres of rope, how many metres of rope can be produced?
✅ Step-by-Step Solution & Working
Working:
• (a) Coir Fibre: (1,500 ÷ 100) × 8 kg = 15 × 8 = 120 kg of coir fibre.
• (b) Rope Length: 120 kg × 15 m/kg = 1,800 metres of rope.
• (a) Coir Fibre: (1,500 ÷ 100) × 8 kg = 15 × 8 = 120 kg of coir fibre.
• (b) Rope Length: 120 kg × 15 m/kg = 1,800 metres of rope.
CBSE Step-by-Step Marking Scheme
Coir fibre = 120 kg
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Rope length = 1,800 m
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Q12
Plantation Layout • Area and Spacing
Coconut trees are planted in a square grid with a spacing of 7 metres between trees.
(a) How many trees are in a row of length 84 metres (including trees at both ends)?
(b) If the orchard is a square of 84 m × 84 m, what is the total number of trees planted?
[3 Marks]
(a) How many trees are in a row of length 84 metres (including trees at both ends)?
(b) If the orchard is a square of 84 m × 84 m, what is the total number of trees planted?
✅ Step-by-Step Solution & Working
Grid Spacing:
• (a) Trees per Row: Number of 7-metre intervals = 84 ÷ 7 = 12 intervals.
- Trees per row = Intervals + 1 (posts and spaces rule) = 12 + 1 = 13 trees.
• (b) Total Trees in Square Orchard: 13 rows × 13 trees/row = 169 trees.
• (a) Trees per Row: Number of 7-metre intervals = 84 ÷ 7 = 12 intervals.
- Trees per row = Intervals + 1 (posts and spaces rule) = 12 + 1 = 13 trees.
• (b) Total Trees in Square Orchard: 13 rows × 13 trees/row = 169 trees.
CBSE Step-by-Step Marking Scheme
12 intervals + 1 = 13 trees per row
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Total trees = 13 × 13 = 169
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Q13
Coconut Tree Growth • Time Progression
A high-yielding dwarf coconut tree begins fruiting in 4 years and produces fruit for 35 years.
(a) For how many years does the tree yield coconuts?
(b) If it produces an average of 140 coconuts annually, how many coconuts will one tree yield over its entire bearing life?
[3 Marks]
(a) For how many years does the tree yield coconuts?
(b) If it produces an average of 140 coconuts annually, how many coconuts will one tree yield over its entire bearing life?
✅ Step-by-Step Solution & Working
Calculations:
• (a) Bearing Period: 35 years.
• (b) Lifetime Yield: 35 years × 140 coconuts/year = 4,900 coconuts.
• (a) Bearing Period: 35 years.
• (b) Lifetime Yield: 35 years × 140 coconuts/year = 4,900 coconuts.
CBSE Step-by-Step Marking Scheme
Bearing period = 35 years
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Lifetime yield: 35 × 140 = 4,900
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Q14
Harvest Cost Breakdown • Net Income
A farmer sells 4,500 coconuts at ₹22 each. His expenses were:
• Tree climber charges: ₹3 per coconut
• Cartage to market: ₹1,500
• Market cess/tax: ₹1,200
(a) Find gross revenue.
(b) Find total expenses.
(c) Find his net profit.
[3 Marks]
• Tree climber charges: ₹3 per coconut
• Cartage to market: ₹1,500
• Market cess/tax: ₹1,200
(a) Find gross revenue.
(b) Find total expenses.
(c) Find his net profit.
✅ Step-by-Step Solution & Working
Financial Calculations:
• (a) Gross Revenue: 4,500 × ₹22 = ₹99,000.
• (b) Total Expenses:
- Climber charges: 4,500 × ₹3 = ₹13,500.
- Cartage = ₹1,500.
- Market cess = ₹1,200.
- Total expenses = ₹13,500 + ₹1,500 + ₹1,200 = ₹16,200.
• (c) Net Profit: ₹99,000 - ₹16,200 = ₹82,800.
• (a) Gross Revenue: 4,500 × ₹22 = ₹99,000.
• (b) Total Expenses:
- Climber charges: 4,500 × ₹3 = ₹13,500.
- Cartage = ₹1,500.
- Market cess = ₹1,200.
- Total expenses = ₹13,500 + ₹1,500 + ₹1,200 = ₹16,200.
• (c) Net Profit: ₹99,000 - ₹16,200 = ₹82,800.
CBSE Step-by-Step Marking Scheme
Gross revenue = ₹99,000
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Total expenses = ₹16,200
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Net profit = ₹82,800
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Q15
Mental Math • Multiplications by 11 and 12
Calculate mentally using shortcuts:
(a) 63 × 11
(b) 45 × 12
(c) 250 × 16
[3 Marks]
(a) 63 × 11
(b) 45 × 12
(c) 250 × 16
✅ Step-by-Step Solution & Working
Shortcuts:
• (a) 63 × 11: Sum of digits = 6 + 3 = 9. Place between: 693.
• (b) 45 × 12: (45 × 10) + (45 × 2) = 450 + 90 = 540.
• (c) 250 × 16: 250 × 4 × 4 = 1,000 × 4 = 4,000.
• (a) 63 × 11: Sum of digits = 6 + 3 = 9. Place between: 693.
• (b) 45 × 12: (45 × 10) + (45 × 2) = 450 + 90 = 540.
• (c) 250 × 16: 250 × 4 × 4 = 1,000 × 4 = 4,000.
CBSE Step-by-Step Marking Scheme
Part (a): 693
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Part (b): 540
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Part (c): 4,000
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Q16
Coconut Shell Crafts • Artisanal Production
A craftsman makes decorative bowls from coconut shells. He can craft 6 bowls in a day. He receives an order for 150 bowls.
(a) How many working days will he take to complete the order?
(b) If he sells each bowl for ₹85, how much will he earn from the entire order?
[3 Marks]
(a) How many working days will he take to complete the order?
(b) If he sells each bowl for ₹85, how much will he earn from the entire order?
✅ Step-by-Step Solution & Working
Working:
• (a) Days Required: 150 ÷ 6 = 25 working days.
• (b) Total Earnings: 150 × ₹85 = ₹12,750.
• (a) Days Required: 150 ÷ 6 = 25 working days.
• (b) Total Earnings: 150 × ₹85 = ₹12,750.
CBSE Step-by-Step Marking Scheme
Days = 25
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Earnings = ₹12,750
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Q17
Division with Zero in Quotient
Solve: $4,208 \div 4$. Show your long division clearly and explain why zero must be written in the hundreds/tens place.
[3 Marks]
✅ Step-by-Step Solution & Working
Long Division Steps:
• Divide thousands: 4 ÷ 4 = 1 (Remainder 0).
• Bring down 2: 2 cannot be divided by 4 (2 < 4). We must write 0 in the quotient.
• Bring down 0 to make 20: 20 ÷ 4 = 5 (Remainder 0).
• Bring down 8: 8 ÷ 4 = 2 (Remainder 0).
Quotient = 1,052, Remainder = 0.
Explanation: Whenever the brought-down digit is smaller than the divisor, a 0 is placed in that place value of the quotient before bringing down the next digit.
• Divide thousands: 4 ÷ 4 = 1 (Remainder 0).
• Bring down 2: 2 cannot be divided by 4 (2 < 4). We must write 0 in the quotient.
• Bring down 0 to make 20: 20 ÷ 4 = 5 (Remainder 0).
• Bring down 8: 8 ÷ 4 = 2 (Remainder 0).
Quotient = 1,052, Remainder = 0.
Explanation: Whenever the brought-down digit is smaller than the divisor, a 0 is placed in that place value of the quotient before bringing down the next digit.
CBSE Step-by-Step Marking Scheme
Correct quotient = 1,052
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Clear explanation for placing 0
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Q18
Coconut Jaggery (Palm Sugar) Yield
From 8 litres of sweet palm sap (neera), 1 kg of palm jaggery is prepared.
(a) How many kilograms of jaggery can be made from 120 litres of sap?
(b) If palm jaggery sells at ₹180 per kg, find the total sales value.
[3 Marks]
(a) How many kilograms of jaggery can be made from 120 litres of sap?
(b) If palm jaggery sells at ₹180 per kg, find the total sales value.
✅ Step-by-Step Solution & Working
Calculations:
• (a) Jaggery Yield: 120 L ÷ 8 L/kg = 15 kg of jaggery.
• (b) Sales Value: 15 kg × ₹180 = ₹2,700.
• (a) Jaggery Yield: 120 L ÷ 8 L/kg = 15 kg of jaggery.
• (b) Sales Value: 15 kg × ₹180 = ₹2,700.
CBSE Step-by-Step Marking Scheme
Jaggery = 15 kg
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Sales value = ₹2,700
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Q19
HOTS • Coconut Division Riddle
A farmer divided a heap of coconuts equally among his 4 sons, and 2 coconuts were left over. When he divided the same heap among 5 neighbours, 2 coconuts were still left over. What is the smallest possible number of coconuts in the heap (greater than 10)?
[3 Marks]
✅ Step-by-Step Solution & Working
LCM and Remainder Principle:
1. The number leaves a remainder of 2 when divided by both 4 and 5.
2. LCM of 4 and 5 = 4 × 5 = 20.
3. The number must be of the form: $\text{LCM}(4, 5) \times k + 2 = 20k + 2$.
4. For $k = 1$: Number = 20 + 2 = 22 coconuts.
5. Verification:
- 22 ÷ 4 = 5 with remainder 2.
- 22 ÷ 5 = 4 with remainder 2.
The smallest possible number of coconuts is 22.
1. The number leaves a remainder of 2 when divided by both 4 and 5.
2. LCM of 4 and 5 = 4 × 5 = 20.
3. The number must be of the form: $\text{LCM}(4, 5) \times k + 2 = 20k + 2$.
4. For $k = 1$: Number = 20 + 2 = 22 coconuts.
5. Verification:
- 22 ÷ 4 = 5 with remainder 2.
- 22 ÷ 5 = 4 with remainder 2.
The smallest possible number of coconuts is 22.
CBSE Step-by-Step Marking Scheme
LCM(4, 5) = 20
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Smallest number = 22 with verification
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Q20
Water Reservoir for Plantation
An irrigation farm pond has a capacity of 48,000 litres. A solar pump fills the pond at the rate of 1,600 litres per hour.
(a) How many hours will the pump take to fill the empty pond completely?
(b) If the pump runs for 6 hours daily, how many days are required?
[3 Marks]
(a) How many hours will the pump take to fill the empty pond completely?
(b) If the pump runs for 6 hours daily, how many days are required?
✅ Step-by-Step Solution & Working
Calculations:
• (a) Total Pumping Hours: 48,000 ÷ 1,600 = 30 hours.
• (b) Days Required: 30 hours ÷ 6 hours/day = 5 days.
• (a) Total Pumping Hours: 48,000 ÷ 1,600 = 30 hours.
• (b) Days Required: 30 hours ÷ 6 hours/day = 5 days.
CBSE Step-by-Step Marking Scheme
30 hours to fill
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5 days at 6 hours/day
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Q21
Coconut Tree Shade • Geometric Area
The fronds of an adult coconut palm cast a circular shadow of radius 3 metres when the sun is overhead.
(a) Approximate the area of shade cast by one tree (take $\pi \approx 3.14$).
(b) If 50 trees cast non-overlapping shade, what is the combined area of shaded ground?
[3 Marks]
(a) Approximate the area of shade cast by one tree (take $\pi \approx 3.14$).
(b) If 50 trees cast non-overlapping shade, what is the combined area of shaded ground?
✅ Step-by-Step Solution & Working
Circular Area Calculations ($A = \pi r^2$):
• (a) Shade per Tree: Area = $3.14 \times 3 \times 3 = 3.14 \times 9 = \mathbf{28.26\text{ sq m}}$.
• (b) 50 Trees: 50 × 28.26 = 1,413 square metres.
• (a) Shade per Tree: Area = $3.14 \times 3 \times 3 = 3.14 \times 9 = \mathbf{28.26\text{ sq m}}$.
• (b) 50 Trees: 50 × 28.26 = 1,413 square metres.
CBSE Step-by-Step Marking Scheme
One tree area = 28.26 sq m
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50 trees = 1,413 sq m
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Q22
Mental Arithmetic • Estimation of Products
Estimate the product by rounding each factor to the nearest ten:
(a) 38 × 52
(b) 69 × 21
(c) 87 × 44
[3 Marks]
(a) 38 × 52
(b) 69 × 21
(c) 87 × 44
✅ Step-by-Step Solution & Working
Estimation Steps:
• (a) 38 × 52: Round 38 → 40; 52 → 50. Estimate = 40 × 50 = 2,000 (Exact = 1,976).
• (b) 69 × 21: Round 69 → 70; 21 → 20. Estimate = 70 × 20 = 1,400 (Exact = 1,449).
• (c) 87 × 44: Round 87 → 90; 44 → 40. Estimate = 90 × 40 = 3,600 (Exact = 3,828).
• (a) 38 × 52: Round 38 → 40; 52 → 50. Estimate = 40 × 50 = 2,000 (Exact = 1,976).
• (b) 69 × 21: Round 69 → 70; 21 → 20. Estimate = 70 × 20 = 1,400 (Exact = 1,449).
• (c) 87 × 44: Round 87 → 90; 44 → 40. Estimate = 90 × 40 = 3,600 (Exact = 3,828).
CBSE Step-by-Step Marking Scheme
Part (a): 2,000
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Part (b): 1,400
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Part (c): 3,600
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Q23
True or False with Arithmetic Reason
State True or False with reasoning:
(a) If a number is divisible by 10, its ones digit must be 0.
(b) $25 \times 48$ is the same as $100 \times 12$.
(c) The remainder in any division problem can be equal to or greater than the divisor.
[3 Marks]
(a) If a number is divisible by 10, its ones digit must be 0.
(b) $25 \times 48$ is the same as $100 \times 12$.
(c) The remainder in any division problem can be equal to or greater than the divisor.
✅ Step-by-Step Solution & Working
Justifications:
• (a) True: All multiples of 10 end with the digit 0.
• (b) True: $25 \times 48 = 25 \times (4 \times 12) = (25 \times 4) \times 12 = 100 \times 12 = 1,200$. Both equal 1,200.
• (c) False: The remainder must strictly be less than the divisor. If it were equal or greater, another division step could be carried out.
• (a) True: All multiples of 10 end with the digit 0.
• (b) True: $25 \times 48 = 25 \times (4 \times 12) = (25 \times 4) \times 12 = 100 \times 12 = 1,200$. Both equal 1,200.
• (c) False: The remainder must strictly be less than the divisor. If it were equal or greater, another division step could be carried out.
CBSE Step-by-Step Marking Scheme
Part (a): True with place value reason
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Part (b): True with associative property
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Part (c): False (remainder must be < divisor)
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Q24
Comprehensive Orchard Harvest Review
Over a 3-month harvest season, a farm records coconut production:
Month 1: 3,450; Month 2: 4,120; Month 3: 3,830.
(a) Find total coconuts harvested.
(b) If 10% of coconuts are kept for domestic consumption and seed, how many are sold in the market?
(c) At ₹20 per coconut, calculate the gross revenue from sales.
[3 Marks]
Month 1: 3,450; Month 2: 4,120; Month 3: 3,830.
(a) Find total coconuts harvested.
(b) If 10% of coconuts are kept for domestic consumption and seed, how many are sold in the market?
(c) At ₹20 per coconut, calculate the gross revenue from sales.
✅ Step-by-Step Solution & Working
Comprehensive Harvest Accounting:
• (a) Total Harvest: 3,450 + 4,120 + 3,830 = 11,400 coconuts.
• (b) Market Sale:
- Domestic share = 10% of 11,400 = 1,140 coconuts.
- Coconuts sold = 11,400 - 1,140 = 10,260 coconuts.
• (c) Gross Revenue: 10,260 × ₹20 = ₹2,05,200.
• (a) Total Harvest: 3,450 + 4,120 + 3,830 = 11,400 coconuts.
• (b) Market Sale:
- Domestic share = 10% of 11,400 = 1,140 coconuts.
- Coconuts sold = 11,400 - 1,140 = 10,260 coconuts.
• (c) Gross Revenue: 10,260 × ₹20 = ₹2,05,200.
CBSE Step-by-Step Marking Scheme
Total = 11,400 coconuts
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Coconuts sold = 10,260
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Gross revenue = ₹2,05,200
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🌟 NEP 2020 Competency-Based Case Study
Competency Question: Coconut Water Cooperative Dispatch
A cooperative dispatches 2,400 tender coconuts to market. 35% are sold directly to street stalls, and the remainder are supplied to juice bottling plants in crates of 24 coconuts each.
Analytical Task: (a) How many coconuts are sold to street stalls?
(b) How many crates are supplied to the bottling plant?
(b) How many crates are supplied to the bottling plant?
Evaluation & Model Answer:
Suggested Model Solution:
(a) Street stalls: 35/100 × 2400 = 840 coconuts.
(b) Bottling crates: 2400 - 840/24 = 1560/24 = 65 crates.
Rubric: 1M concept identification + 1M step execution + 1M conclusion