Chapter 12 of 14
Chapter 12: Ticking Clocks and Turning Calendar
12-Hour vs. 24-Hour Clocks, AM/PM, Elapsed Time & Calendar Logic | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Reading time to the exact minute on analog and digital clocks.
- Converting between 12-hour (am/pm) and 24-hour railway time formats.
- Calculating elapsed time (start time, end time, duration).
- Understanding calendar months, leap years, manufacturing and expiry dates on packaged products.
All Textbook Exercises & In-Text Tasks (15 Questions)
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Q1
Time Conversion & Calculation
Convert to 24-hour clock time: (a) 6:15 am, (b) 2:45 pm, (c) 11:20 pm, (d) 12:00 midnight. (e) If a train departs at 08:45 and arrives at 14:15, what is the journey duration?
[4 Marks]
✅ Step-by-Step Solution & Working
Part 1: Conversions to 24-Hour Time:
• (a) 6:15 am = 06:15 hours (am times before noon remain unchanged).
• (b) 2:45 pm = 2:45 + 12:00 = 14:45 hours.
• (c) 11:20 pm = 11:20 + 12:00 = 23:20 hours.
• (d) 12:00 midnight = 00:00 hours (or 24:00 hours).
Part 2: Train Journey Duration:
• Departure: 08:45 hours.
• From 08:45 to 09:00 = 15 minutes.
• From 09:00 to 14:00 = 5 hours.
• From 14:00 to 14:15 = 15 minutes.
• Total duration = 5 hours + 15 min + 15 min = 5 hours 30 minutes.
• (a) 6:15 am = 06:15 hours (am times before noon remain unchanged).
• (b) 2:45 pm = 2:45 + 12:00 = 14:45 hours.
• (c) 11:20 pm = 11:20 + 12:00 = 23:20 hours.
• (d) 12:00 midnight = 00:00 hours (or 24:00 hours).
Part 2: Train Journey Duration:
• Departure: 08:45 hours.
• From 08:45 to 09:00 = 15 minutes.
• From 09:00 to 14:00 = 5 hours.
• From 14:00 to 14:15 = 15 minutes.
• Total duration = 5 hours + 15 min + 15 min = 5 hours 30 minutes.
CBSE Step-by-Step Marking Scheme
Correct conversions for all 4 time formats
2.0 M
Accurate step-by-step elapsed time calculation (5h 30m)
2.0 M
Q2
Time Arithmetic • 24-Hour Railway Clock
Convert the following times between 12-hour clock (am/pm) and 24-hour railway clock:
(a) 07:45 am
(b) 03:20 pm
(c) 21:50 hours
[3 Marks]
(a) 07:45 am
(b) 03:20 pm
(c) 21:50 hours
✅ Step-by-Step Solution & Working
Time Conversions:
• (a) 07:45 am: Since it is am before noon, the time remains 07:45 hours.
• (b) 03:20 pm: Since it is pm after noon, add 12 hours: 3:20 + 12:00 = 15:20 hours.
• (c) 21:50 hours: Since it is greater than 12:00, subtract 12 hours: 21:50 - 12:00 = 09:50 pm.
• (a) 07:45 am: Since it is am before noon, the time remains 07:45 hours.
• (b) 03:20 pm: Since it is pm after noon, add 12 hours: 3:20 + 12:00 = 15:20 hours.
• (c) 21:50 hours: Since it is greater than 12:00, subtract 12 hours: 21:50 - 12:00 = 09:50 pm.
CBSE Step-by-Step Marking Scheme
(a) 07:45 hours
1.0 M
(b) 15:20 hours
1.0 M
(c) 09:50 pm
1.0 M
Q3
Elapsed Time • Journey Duration
A superfast train departs from New Delhi at 06:15 am and arrives in Amritsar on the same day at 01:45 pm. What is the total duration of the train journey?
[3 Marks]
✅ Step-by-Step Solution & Working
Elapsed Time Calculation:
• Departure Time: 06:15 am
• Arrival Time: 01:45 pm
1. From 06:15 am to 12:15 pm (noon) = 6 hours.
2. From 12:15 pm to 01:15 pm = 1 hour.
3. From 01:15 pm to 01:45 pm = 30 minutes.
Total Journey Time = 6 hours + 1 hour + 30 minutes = 7 hours 30 minutes.
• Departure Time: 06:15 am
• Arrival Time: 01:45 pm
1. From 06:15 am to 12:15 pm (noon) = 6 hours.
2. From 12:15 pm to 01:15 pm = 1 hour.
3. From 01:15 pm to 01:45 pm = 30 minutes.
Total Journey Time = 6 hours + 1 hour + 30 minutes = 7 hours 30 minutes.
CBSE Step-by-Step Marking Scheme
Decomposing time to noon milestone
1.5 M
Accurate sum: 7 hours 30 minutes
1.5 M
Q4
Calendar Literacy • Expiry Dates
A packet of butter shows 'Manufacture Date: 15/04/2026' and 'Best before 180 days from packaging'. Can it be safely consumed on 15th October 2026? Show calculations.
[3 Marks]
✅ Step-by-Step Solution & Working
Days Count Calculation:
• Days remaining in April (after 15th): 30 - 15 = 15 days.
• May: 31 days.
• June: 30 days.
• July: 31 days.
• August: 31 days.
• September: 30 days.
• Total days elapsed by Sept 30 = 15 + 31 + 30 + 31 + 31 + 30 = 168 days.
Remaining valid days for October = 180 - 168 = 12 days.
Hence, the product expires on 12th October 2026.
Therefore, on 15th October 2026 (183 days), the butter is expired and unsafe to consume.
• Days remaining in April (after 15th): 30 - 15 = 15 days.
• May: 31 days.
• June: 30 days.
• July: 31 days.
• August: 31 days.
• September: 30 days.
• Total days elapsed by Sept 30 = 15 + 31 + 30 + 31 + 31 + 30 = 168 days.
Remaining valid days for October = 180 - 168 = 12 days.
Hence, the product expires on 12th October 2026.
Therefore, on 15th October 2026 (183 days), the butter is expired and unsafe to consume.
CBSE Step-by-Step Marking Scheme
Accurate month-by-month day counting (168 days up to Sept 30)
1.5 M
Calculating expiry on Oct 12 and concluding unsafe on Oct 15
1.5 M
Q5
Textbook Exercise • Real-World Context
In Chapter 12 ('Ticking Clocks and Turning Calendar'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Practice Time • Measurement & Conversions
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
[3 Marks]
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
✅ Step-by-Step Solution & Working
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Try These • Geometry and Shapes
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have?
[3 Marks]
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have?
✅ Step-by-Step Solution & Working
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
Money & Accounts • Rate List Calculation
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns?
[3 Marks]
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns?
✅ Step-by-Step Solution & Working
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
Fractions Exploration • Parts of a Whole
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena?
[3 Marks]
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena?
✅ Step-by-Step Solution & Working
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
Time & Clocks • Elapsed Time
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
[3 Marks]
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
✅ Step-by-Step Solution & Working
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
Perimeter & Area • Fencing a Field
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing.
[3 Marks]
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing.
✅ Step-by-Step Solution & Working
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Mental Math • Division and Multiplication
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ?
[2 Marks]
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ?
✅ Step-by-Step Solution & Working
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Patterns & Symmetries • Rotational Turns
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)?
[2 Marks]
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)?
✅ Step-by-Step Solution & Working
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
Smart Charts • Data Interpretation
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
[3 Marks]
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
✅ Step-by-Step Solution & Working
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
Chapter Review • True or False
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth).
[3 Marks]
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth).
✅ Step-by-Step Solution & Working
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study
Medicine Expiry Date Verification
A medicine bottle has manufacturing date 'MFG: 03/24' and states 'Best before 24 months from manufacture'.
Analytical Task: Can this medicine be safely consumed in February 2026? What is the last safe month?
Evaluation & Model Answer:
Analysis:
• Manufacturing date = March 2024 (03/24).
• Adding 24 months (2 full years): March 2024 + 2 years = March 2026.
Conclusion:
Yes, it can be safely consumed in February 2026 because February 2026 falls before the expiry date of March 2026.
• Manufacturing date = March 2024 (03/24).
• Adding 24 months (2 full years): March 2024 + 2 years = March 2026.
Conclusion:
Yes, it can be safely consumed in February 2026 because February 2026 falls before the expiry date of March 2026.
Rubric: 1 Mark for calculating expiry month (March 2026); 1 Mark for valid consumption conclusion.