NCERT Class 4 Mathematics • Classic CBSE Track

Chapter 2: Long and Short

Q: Look at the athletic records: Javier S. holds the Men's World Record for High Jump at 2 m 45 cm. Chandrapal holds the Indian Record for High Jump at 2

(a) Difference between World and Indian High Jump records: • Javier S. (World Record) = 2 m 45 cm = 245 cm. • Chandrapal (Indian Record) = 2 m 17 cm = 217 cm. • Difference = 245 cm - 217 cm = 28 cm. Chandrapal must jump 28 cm higher. (b) Short of 2 and a half metres (2 m 50 cm): • 2 and a half metre

Q: A stadium running track is 400 metres long for one complete lap. People run a marathon race of 40 kilometres. How many complete rounds of the stadium

Step 1: Convert marathon distance into metres: • 1 kilometre = 1,000 metres. • 40 km = 40 × 1,000 = 40,000 metres. Step 2: Calculate number of rounds: • Length of 1 round of stadium = 400 metres. • Number of rounds = Total distance ÷ Track length • Number of rounds = 40,000 ÷ 400 = 100 rounds. A run

Q: In high jump, Javier S. holds the world record of 2 m 45 cm, and Chandra Pal holds the Indian record of 2 m 17 cm. How many centimetres higher must Ch

Difference Calculation: • World Record = 2 m 45 cm = 245 cm • Indian Record = 2 m 17 cm = 217 cm Difference = 245 cm - 217 cm = 28 cm. Chandra Pal must jump 28 centimetres higher to equal the world record.

Q: A doctor tells Devi Prasad to run 2 km every day to stay fit. He runs around a square field with each side 500 metres long. (a) How many rounds of thi

Step-by-Step Solution (Target = 2 km = 2,000 m): 1. (a) Square Field: • Side = 500 m • Perimeter of square = 4 × 500 m = 2,000 m. • Number of rounds = 2,000 m ÷ 2,000 m = 1 round. 2. (b) 400-metre Stadium Track: • Number of rounds = 2,000 m ÷ 400 m = 5 rounds.

Q: 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 ma

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.

Q: 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) H

Step-by-Step Solution:• (a) Total diesel: 4 buses × 50 L = 200 litres.• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.

Q: 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)

Calculations:• (a) High Jump: 245 cm = 2 metres 45 centimetres.• (b) Difference: 250 cm - 245 cm = 5 centimetres.

Q: 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.

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.

Q: 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 t

Loan Repayment:• (a) Total paid: 6 months × ₹51/month = ₹306.• (b) Extra money (interest): ₹306 - ₹300 = ₹6.

Q: 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

Dosage Calculations:• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.

Measuring Heights, Distances, Conversions (cm, m, km), Sports Records & Marathon Math | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts

Comparing lengths visually and measuring accurately using a ruler and measuring tape.
Units of length: 1 m = 100 cm; 1 km = 1,000 m.
Analyzing world records and Indian records in high jump and long jump.
Calculating distances in round tracks and solving marathon running problems.

All Textbook Exercises & In-Text Tasks (15 Questions)

100% Complete Ingestion

Q1 Sports Records Comparison

Look at the athletic records: Javier S. holds the Men's World Record for High Jump at 2 m 45 cm. Chandrapal holds the Indian Record for High Jump at 2 m 17 cm. (a) How many more centimetres must Chandrapal jump to equal Javier's world record? (b) How many centimetres short of 2 and a half metres is Javier's jump?

[3 Marks]

✅ Step-by-Step Solution & Working

(a) Difference between World and Indian High Jump records:
• Javier S. (World Record) = 2 m 45 cm = 245 cm.
• Chandrapal (Indian Record) = 2 m 17 cm = 217 cm.
• Difference = 245 cm - 217 cm = 28 cm.
Chandrapal must jump 28 cm higher.

(b) Short of 2 and a half metres (2 m 50 cm):
• 2 and a half metres = 2 m 50 cm = 250 cm.
• Javier's jump = 245 cm.
• Difference = 250 cm - 245 cm = 5 cm.
Javier's jump is only 5 cm short of 2.5 metres.

CBSE Step-by-Step Marking Scheme

Correct difference of 28 cm with conversion 1.5 M

Correct calculation showing 5 cm short of 2.5 m 1.5 M

Q2 Marathon & Stadium Track Math

A stadium running track is 400 metres long for one complete lap. People run a marathon race of 40 kilometres. How many complete rounds of the stadium track must a runner make to complete the 40 km marathon?

[3 Marks]

✅ Step-by-Step Solution & Working

Step 1: Convert marathon distance into metres:
• 1 kilometre = 1,000 metres.
• 40 km = 40 × 1,000 = 40,000 metres.

Step 2: Calculate number of rounds:
• Length of 1 round of stadium = 400 metres.
• Number of rounds = Total distance ÷ Track length
• Number of rounds = 40,000 ÷ 400 = 100 rounds.

A runner must complete exactly 100 rounds of the stadium track.

CBSE Step-by-Step Marking Scheme

Unit conversion 40 km = 40,000 m 1.5 M

Division 40,000 ÷ 400 = 100 rounds 1.5 M

Q3 Sports Arithmetic • High Jump & Long Jump

In high jump, Javier S. holds the world record of 2 m 45 cm, and Chandra Pal holds the Indian record of 2 m 17 cm. How many centimetres higher must Chandra Pal jump to equal the world record?

[2 Marks]

✅ Step-by-Step Solution & Working

Difference Calculation:
• World Record = 2 m 45 cm = 245 cm
• Indian Record = 2 m 17 cm = 217 cm

Difference = 245 cm - 217 cm = 28 cm.

Chandra Pal must jump 28 centimetres higher to equal the world record.

CBSE Step-by-Step Marking Scheme

Conversion to centimetres (245 cm and 217 cm) 1.0 M

Correct difference of 28 cm 1.0 M

Q4 Marathon & Distance • Stadium Track

A doctor tells Devi Prasad to run 2 km every day to stay fit. He runs around a square field with each side 500 metres long. (a) How many rounds of this field must he take to complete 2 km? (b) If he instead runs on a 400-metre circular stadium track, how many rounds are needed?

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Solution (Target = 2 km = 2,000 m):
1. (a) Square Field:
• Side = 500 m
• Perimeter of square = 4 × 500 m = 2,000 m.
• Number of rounds = 2,000 m ÷ 2,000 m = 1 round.

2. (b) 400-metre Stadium Track:
• Number of rounds = 2,000 m ÷ 400 m = 5 rounds.

CBSE Step-by-Step Marking Scheme

Square field perimeter (2,000 m) = 1 round 1.5 M

Stadium track calculation: 2,000 ÷ 400 = 5 rounds 1.5 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]

✅ 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.

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]

✅ 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.

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]

✅ Step-by-Step Solution & Working

Calculations:
• (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.

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]

✅ Step-by-Step Solution & Working

Loan Repayment:
• (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]

✅ 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.

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]

✅ 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.

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]

✅ 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.

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]

✅ Step-by-Step Solution & Working

Decoding Cipher:
• 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]

✅ 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.

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]

✅ 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.

CBSE Step-by-Step Marking Scheme

True, False, True with explanations 3 M

🌟 NEP 2020 Competency-Based Case Study

Daily Walking Distance Goal

Doctor advises grandfather to walk 2 kilometres every day to stay fit. Grandfather walks around a square park that measures 125 metres on each side.

Analytical Task: How many complete rounds of the park must grandfather take to achieve his 2 km goal?

Evaluation & Model Answer:

Step 1: Perimeter of square park:
Perimeter = 4 × 125 m = 500 metres per round.
Step 2: Rounds for 2 km:
2 km = 2,000 metres.
Rounds required = 2,000 m ÷ 500 m = 4 rounds.
Grandfather must walk 4 complete rounds.

Rubric: 1 Mark for park perimeter 500 m; 1 Mark for 4 rounds.