Chapter 12 of 14
Chapter 12: How Heavy? How Light?
Pan Balance Weighing, Grams & Kilograms, Postal Tariffs & Weight Estimation | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Comparing weights using a beam balance scale.
- 1 Kilogram (kg) = 1,000 Grams (g); 1/2 kg = 500 g; 1/4 kg = 250 g.
- Indian Post Office parcel and letter tariff rates based on weight increments.
- Estimating weights of heavy objects (elephant, tractor, sack of wheat) vs light objects (pencil, feather).
All Textbook Exercises & In-Text Tasks (15 Questions)
100% Complete Ingestion
Q1
Postal Tariff Calculation
Look at the postal rates: A parcel weighing 50 grams or less costs ₹5. For every additional 50 grams or part thereof, it costs ₹3. Radha wants to send a book parcel weighing 225 grams to her friend. How much postal stamp value must she affix on the parcel?
[3 Marks]
✅ Step-by-Step Solution & Working
Step 1: Break down the weight of 225 grams into 50 g slabs:
• First 50 grams = 50 g (remaining = 225 - 50 = 175 g).
• Next 50 grams = 50 g (remaining = 125 g).
• Next 50 grams = 50 g (remaining = 75 g).
• Next 50 grams = 50 g (remaining = 25 g).
• Final 25 grams counts as an additional 50 g slab.
Total slabs = 1 basic slab + 4 additional slabs.
Step 2: Calculate cost:
• First 50 g = ₹5.
• 4 additional slabs of 50 g = 4 × ₹3 = ₹12.
• Total postal stamp value = ₹5 + ₹12 = ₹17.
• First 50 grams = 50 g (remaining = 225 - 50 = 175 g).
• Next 50 grams = 50 g (remaining = 125 g).
• Next 50 grams = 50 g (remaining = 75 g).
• Next 50 grams = 50 g (remaining = 25 g).
• Final 25 grams counts as an additional 50 g slab.
Total slabs = 1 basic slab + 4 additional slabs.
Step 2: Calculate cost:
• First 50 g = ₹5.
• 4 additional slabs of 50 g = 4 × ₹3 = ₹12.
• Total postal stamp value = ₹5 + ₹12 = ₹17.
CBSE Step-by-Step Marking Scheme
Correct breakdown of 225 g into 5 slabs
1.5 M
Accurate calculation giving ₹17 stamp cost
1.5 M
Q2
Postal Mathematics • Calculating Postage
Look at the postal rates:
• Single letter (up to 20 g): ₹5.00
• For every additional 20 g: ₹2.00
Calculate the postage stamps required to send a heavy official letter weighing 75 grams.
[3 Marks]
• Single letter (up to 20 g): ₹5.00
• For every additional 20 g: ₹2.00
Calculate the postage stamps required to send a heavy official letter weighing 75 grams.
✅ Step-by-Step Solution & Working
Step-by-Step Postal Calculation:
Total weight = 75 grams.
1. First 20 grams: Cost = ₹5.00.
2. Remaining weight: 75 g - 20 g = 55 grams.
• Next 20 g (21–40 g): + ₹2.00
• Next 20 g (41–60 g): + ₹2.00
• Remaining 15 g (part of next 20 g, 61–75 g): + ₹2.00
Total additional 20 g units = 3 units.
Additional cost = 3 × ₹2.00 = ₹6.00.
Total Postage Required:
₹5.00 + ₹6.00 = ₹11.00.
Total weight = 75 grams.
1. First 20 grams: Cost = ₹5.00.
2. Remaining weight: 75 g - 20 g = 55 grams.
• Next 20 g (21–40 g): + ₹2.00
• Next 20 g (41–60 g): + ₹2.00
• Remaining 15 g (part of next 20 g, 61–75 g): + ₹2.00
Total additional 20 g units = 3 units.
Additional cost = 3 × ₹2.00 = ₹6.00.
Total Postage Required:
₹5.00 + ₹6.00 = ₹11.00.
CBSE Step-by-Step Marking Scheme
Base charge for first 20 g (₹5.00)
1.0 M
Identifying 3 additional units (₹6.00)
1.0 M
Total postage: ₹11.00
1.0 M
Q3
Weight Estimation • Grams vs. Kilograms
State whether the following objects should be measured in 'grams' or 'kilograms':
(a) A tube of toothpaste
(b) A sack of rice
(c) A golden ring
(d) A newborn baby
[2 Marks]
(a) A tube of toothpaste
(b) A sack of rice
(c) A golden ring
(d) A newborn baby
✅ Step-by-Step Solution & Working
Units of Weight:
• (a) A tube of toothpaste: Grams (g) (approx. 100 g - 150 g)
• (b) A sack of rice: Kilograms (kg) (approx. 25 kg - 50 kg)
• (c) A golden ring: Grams (g) (approx. 4 g - 8 g)
• (d) A newborn baby: Kilograms (kg) (approx. 2.5 kg - 3.5 kg).
• (a) A tube of toothpaste: Grams (g) (approx. 100 g - 150 g)
• (b) A sack of rice: Kilograms (kg) (approx. 25 kg - 50 kg)
• (c) A golden ring: Grams (g) (approx. 4 g - 8 g)
• (d) A newborn baby: Kilograms (kg) (approx. 2.5 kg - 3.5 kg).
CBSE Step-by-Step Marking Scheme
All four units correctly identified
2.0 M
Q4
Weight Conversion • Balancing Scales
How many 250-gram packets of tea make 1 1/2 kilograms?
[2 Marks]
✅ Step-by-Step Solution & Working
Calculation:
1. Convert 1 1/2 kg into grams:
1 kg = 1,000 g
1/2 kg = 500 g
Total weight = 1,000 g + 500 g = 1,500 grams.
2. Number of 250 g packets:
1,500 ÷ 250 = 6 packets.
Exactly 6 packets of tea make 1 1/2 kg.
1. Convert 1 1/2 kg into grams:
1 kg = 1,000 g
1/2 kg = 500 g
Total weight = 1,000 g + 500 g = 1,500 grams.
2. Number of 250 g packets:
1,500 ÷ 250 = 6 packets.
Exactly 6 packets of tea make 1 1/2 kg.
CBSE Step-by-Step Marking Scheme
Conversion to 1,500 g
1.0 M
Division: 1500 ÷ 250 = 6 packets
1.0 M
Q5
Building with Bricks • Brick Geometry & Measurement
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long?
[3 Marks]
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long?
✅ Step-by-Step Solution & Working
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
A Trip to Bhopal • Diesel Fuel Budget
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay?
[3 Marks]
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay?
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
Long and Short • Height Comparisons
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)?
[2 Marks]
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)?
✅ Step-by-Step Solution & Working
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
Tick-Tick-Tick • Expiry Dates on Food
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
[2 Marks]
✅ Step-by-Step Solution & Working
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
The Junk Seller • Loan and Interest
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank?
[3 Marks]
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank?
✅ Step-by-Step Solution & Working
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
Jugs and Mugs • Measuring Medicine Dose
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last?
[3 Marks]
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last?
✅ Step-by-Step Solution & Working
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
Carts and Wheels • Circle Geometry
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle?
[2 Marks]
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle?
✅ Step-by-Step Solution & Working
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Halves and Quarters • Fraction Sharing
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left?
[3 Marks]
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left?
✅ Step-by-Step Solution & Working
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
Play with Patterns • Secret Message Cipher
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell?
[2 Marks]
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell?
✅ Step-by-Step Solution & Working
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
Tables and Shares • Division with Remainder
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over?
[2 Marks]
(a) How many complete bouquets can she make?
(b) How many roses will be left over?
✅ Step-by-Step Solution & Working
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
Review Questions • True or False
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time.
[3 Marks]
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time.
✅ Step-by-Step Solution & Working
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study
Balancing Scales with Broken Stone Weights
A vendor had a single 4 kg stone weight. It broke into two pieces of 1 kg and 3 kg.
Analytical Task: How can the vendor weigh out exactly 2 kg of firewood using these two pieces on a two-pan balance?
Evaluation & Model Answer:
Procedure:
• Place the 3 kg piece on the left pan.
• Place the 1 kg piece on the right pan.
• Add firewood to the right pan until both pans balance in equilibrium.
• Since Left Pan (3 kg) = Right Pan (1 kg + Firewood), the weight of firewood is 3 kg - 1 kg = 2 kg.
• Place the 3 kg piece on the left pan.
• Place the 1 kg piece on the right pan.
• Add firewood to the right pan until both pans balance in equilibrium.
• Since Left Pan (3 kg) = Right Pan (1 kg + Firewood), the weight of firewood is 3 kg - 1 kg = 2 kg.
Rubric: 1.5 Marks for correct pan placement; 1.5 Marks for mathematical balance proof.