Chapter 12 of 15
Chapter 12: Racing Seconds
दौड़ते सेकंड (समय, सेकंड-मिनट-घंटे, डिजिटल स्टॉपवॉच एवं 24-घंटे घड़ी) | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Units of time: 1 hour = 60 minutes; 1 minute = 60 seconds; 1 hour = 3,600 seconds.
- Elapsed Time: Elapsed Time = Finish Time - Start Time.
- 24-Hour Railway Clock: 1:00 PM = 13:00, 4:30 PM = 16:30, 11:45 PM = 23:45.
- Precision timekeeping with stopwatches (seconds and fractions of seconds).
All Textbook Exercises & In-Text Tasks (24 Questions)
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Q1
Time Unit Conversions • Hours & Minutes
Convert:
(a) 3 hours 25 minutes into minutes.
(b) 280 minutes into hours and minutes.
(c) 4 minutes 45 seconds into seconds.
(d) 350 seconds into minutes and seconds.
[3 Marks]
(a) 3 hours 25 minutes into minutes.
(b) 280 minutes into hours and minutes.
(c) 4 minutes 45 seconds into seconds.
(d) 350 seconds into minutes and seconds.
✅ Step-by-Step Solution & Working
Conversions:
• (a) 3 h 25 min: (3 × 60) + 25 = 180 + 25 = 205 minutes.
• (b) 280 min: 280 ÷ 60 gives quotient 4 with remainder 40 → 4 hours 40 minutes.
• (c) 4 min 45 s: (4 × 60) + 45 = 240 + 45 = 285 seconds.
• (d) 350 s: 350 ÷ 60 gives quotient 5 with remainder 50 → 5 minutes 50 seconds.
• (a) 3 h 25 min: (3 × 60) + 25 = 180 + 25 = 205 minutes.
• (b) 280 min: 280 ÷ 60 gives quotient 4 with remainder 40 → 4 hours 40 minutes.
• (c) 4 min 45 s: (4 × 60) + 45 = 240 + 45 = 285 seconds.
• (d) 350 s: 350 ÷ 60 gives quotient 5 with remainder 50 → 5 minutes 50 seconds.
CBSE Step-by-Step Marking Scheme
Part (a): 205 minutes
0.75 M
Part (b): 4 h 40 min
0.75 M
Part (c): 285 seconds
0.75 M
Part (d): 5 min 50 s
0.75 M
Q2
Stopwatch Timing • 100-Metre Sprint
A school sports day 100-metre race started at 10:42:15 AM and finished at 10:42:29 AM.
(a) What was the race duration recorded on the electronic timer?
(b) If the second runner finished in 15.6 seconds, by how many seconds did the winner win?
[3 Marks]
(a) What was the race duration recorded on the electronic timer?
(b) If the second runner finished in 15.6 seconds, by how many seconds did the winner win?
✅ Step-by-Step Solution & Working
Timing Calculations:
• (a) Winner's Time: 10:42:29 - 10:42:15 = 14 seconds.
• (b) Winning Margin: 15.6 s - 14.0 s = 1.6 seconds.
• (a) Winner's Time: 10:42:29 - 10:42:15 = 14 seconds.
• (b) Winning Margin: 15.6 s - 14.0 s = 1.6 seconds.
CBSE Step-by-Step Marking Scheme
Winner's time = 14 seconds
1.5 M
Margin = 1.6 seconds
1.5 M
Q3
Elapsed Time • Film Show Duration
A family film screening at a multiplex begins at 3:15 PM and ends at 5:50 PM. There is a 15-minute intermission in between.
(a) Find the total elapsed time from start to end.
(b) What was the actual playing time of the movie without intermission?
[3 Marks]
(a) Find the total elapsed time from start to end.
(b) What was the actual playing time of the movie without intermission?
✅ Step-by-Step Solution & Working
Working:
• (a) Total Duration: 3:15 PM to 5:15 PM is 2 hours; 5:15 PM to 5:50 PM is 35 minutes. Total = 2 hours 35 minutes (155 minutes).
• (b) Movie Playing Time: 155 min - 15 min intermission = 140 minutes = 2 hours 20 minutes.
• (a) Total Duration: 3:15 PM to 5:15 PM is 2 hours; 5:15 PM to 5:50 PM is 35 minutes. Total = 2 hours 35 minutes (155 minutes).
• (b) Movie Playing Time: 155 min - 15 min intermission = 140 minutes = 2 hours 20 minutes.
CBSE Step-by-Step Marking Scheme
Total duration = 2 h 35 min
1.5 M
Movie runtime = 2 h 20 min
1.5 M
Q4
12-Hour vs 24-Hour Railway Time
Convert between 12-hour AM/PM and 24-hour Railway Time:
(a) 8:20 AM
(b) 7:45 PM
(c) 14:15 hours
(d) 23:50 hours
[3 Marks]
(a) 8:20 AM
(b) 7:45 PM
(c) 14:15 hours
(d) 23:50 hours
✅ Step-by-Step Solution & Working
Time Format Conversions:
• (a) 8:20 AM: 08:20 hours.
• (b) 7:45 PM: 7:45 + 12:00 = 19:45 hours.
• (c) 14:15 hours: 14:15 - 12:00 = 2:15 PM.
• (d) 23:50 hours: 23:50 - 12:00 = 11:50 PM.
• (a) 8:20 AM: 08:20 hours.
• (b) 7:45 PM: 7:45 + 12:00 = 19:45 hours.
• (c) 14:15 hours: 14:15 - 12:00 = 2:15 PM.
• (d) 23:50 hours: 23:50 - 12:00 = 11:50 PM.
CBSE Step-by-Step Marking Scheme
Parts (a) & (b): 08:20, 19:45
1.5 M
Parts (c) & (d): 2:15 PM, 11:50 PM
1.5 M
Q5
Railway Timetable Duration Analysis
The Vande Bharat Express departs from New Delhi at 06:00 hours and arrives in Varanasi at 14:00 hours.
(a) How many hours does the journey take?
(b) If the distance is 760 km, what is the train's average speed?
[3 Marks]
(a) How many hours does the journey take?
(b) If the distance is 760 km, what is the train's average speed?
✅ Step-by-Step Solution & Working
Calculations:
• (a) Journey Time: 14:00 - 06:00 = 8 hours.
• (b) Average Speed: Speed = Distance ÷ Time = 760 km ÷ 8 h = 95 km/h.
• (a) Journey Time: 14:00 - 06:00 = 8 hours.
• (b) Average Speed: Speed = Distance ÷ Time = 760 km ÷ 8 h = 95 km/h.
CBSE Step-by-Step Marking Scheme
Journey time = 8 hours
1.5 M
Speed = 95 km/h
1.5 M
Q6
Heartbeat Count • Pulse Measurement
A healthy 10-year-old child's heart beats 75 times per minute at rest.
(a) How many times does the heart beat in 1 hour?
(b) How many times does it beat in a full day of 24 hours?
[3 Marks]
(a) How many times does the heart beat in 1 hour?
(b) How many times does it beat in a full day of 24 hours?
✅ Step-by-Step Solution & Working
Heartbeat Calculations:
• (a) In 1 Hour (60 min): 75 × 60 = 4,500 beats per hour.
• (b) In 24 Hours: 4,500 × 24 = 1,08,000 beats per day.
• (a) In 1 Hour (60 min): 75 × 60 = 4,500 beats per hour.
• (b) In 24 Hours: 4,500 × 24 = 1,08,000 beats per day.
CBSE Step-by-Step Marking Scheme
1 hour = 4,500 beats
1.5 M
24 hours = 1,08,000 beats
1.5 M
Q7
Adding Time Intervals
Add the following time periods:
(a) 2 hours 45 minutes + 3 hours 35 minutes
(b) 1 hour 50 minutes 40 seconds + 2 hours 25 minutes 35 seconds
[3 Marks]
(a) 2 hours 45 minutes + 3 hours 35 minutes
(b) 1 hour 50 minutes 40 seconds + 2 hours 25 minutes 35 seconds
✅ Step-by-Step Solution & Working
Addition with Regrouping:
• (a) Hours and Minutes:
- Minutes: 45 + 35 = 80 min = 1 h 20 min.
- Hours: 2 + 3 + 1 = 6 hours.
- Total = 6 hours 20 minutes.
• (b) Hours, Minutes, Seconds:
- Seconds: 40 + 35 = 75 s = 1 min 15 s.
- Minutes: 50 + 25 + 1 = 76 min = 1 h 16 min.
- Hours: 1 + 2 + 1 = 4 hours.
- Total = 4 hours 16 minutes 15 seconds.
• (a) Hours and Minutes:
- Minutes: 45 + 35 = 80 min = 1 h 20 min.
- Hours: 2 + 3 + 1 = 6 hours.
- Total = 6 hours 20 minutes.
• (b) Hours, Minutes, Seconds:
- Seconds: 40 + 35 = 75 s = 1 min 15 s.
- Minutes: 50 + 25 + 1 = 76 min = 1 h 16 min.
- Hours: 1 + 2 + 1 = 4 hours.
- Total = 4 hours 16 minutes 15 seconds.
CBSE Step-by-Step Marking Scheme
Part (a): 6 h 20 min
1.5 M
Part (b): 4 h 16 min 15 s
1.5 M
Q8
Subtracting Time Intervals
Subtract:
(a) 5 hours 20 minutes - 2 hours 45 minutes
(b) 8 hours 15 minutes - 4 hours 50 minutes
[3 Marks]
(a) 5 hours 20 minutes - 2 hours 45 minutes
(b) 8 hours 15 minutes - 4 hours 50 minutes
✅ Step-by-Step Solution & Working
Subtraction with Borrowing (1 Hour = 60 Minutes):
• (a) 5 h 20 min - 2 h 45 min:
- Borrow 1 h (60 min): 20 + 60 = 80 min.
- 80 - 45 = 35 minutes.
- Hours: 4 - 2 = 2 hours.
- Result = 2 hours 35 minutes.
• (b) 8 h 15 min - 4 h 50 min:
- Borrow 1 h: 15 + 60 = 75 min.
- 75 - 50 = 25 minutes.
- Hours: 7 - 4 = 3 hours.
- Result = 3 hours 25 minutes.
• (a) 5 h 20 min - 2 h 45 min:
- Borrow 1 h (60 min): 20 + 60 = 80 min.
- 80 - 45 = 35 minutes.
- Hours: 4 - 2 = 2 hours.
- Result = 2 hours 35 minutes.
• (b) 8 h 15 min - 4 h 50 min:
- Borrow 1 h: 15 + 60 = 75 min.
- 75 - 50 = 25 minutes.
- Hours: 7 - 4 = 3 hours.
- Result = 3 hours 25 minutes.
CBSE Step-by-Step Marking Scheme
Part (a): 2 h 35 min
1.5 M
Part (b): 3 h 25 min
1.5 M
Q9
School Daily Timetable • Period Duration
A school day runs from 8:00 AM to 2:00 PM. It has morning assembly (20 minutes), two breaks of 15 minutes and 25 minutes, and 8 equal study periods.
(a) What is the total duration of the school day?
(b) What is the total non-instructional time (assembly + breaks)?
(c) How many minutes long is each study period?
[3 Marks]
(a) What is the total duration of the school day?
(b) What is the total non-instructional time (assembly + breaks)?
(c) How many minutes long is each study period?
✅ Step-by-Step Solution & Working
Timetable Analysis:
• (a) Total School Duration: 8:00 AM to 2:00 PM = 6 hours = 360 minutes.
• (b) Non-Instructional Time: 20 min + 15 min + 25 min = 60 minutes (1 hour).
• (c) Study Period Duration:
- Instructional time = 360 - 60 = 300 minutes.
- 8 periods: 300 ÷ 8 = 37.5 minutes (37 minutes 30 seconds per period).
• (a) Total School Duration: 8:00 AM to 2:00 PM = 6 hours = 360 minutes.
• (b) Non-Instructional Time: 20 min + 15 min + 25 min = 60 minutes (1 hour).
• (c) Study Period Duration:
- Instructional time = 360 - 60 = 300 minutes.
- 8 periods: 300 ÷ 8 = 37.5 minutes (37 minutes 30 seconds per period).
CBSE Step-by-Step Marking Scheme
Total time = 360 min
1.0 M
Non-instructional = 60 min
1.0 M
Each period = 37.5 min
1.0 M
Q10
Second Pendulum • Frequency & Beats
A grandfather clock pendulum takes 1 second to swing from one side to the other (half period), making one complete back-and-forth oscillation every 2 seconds.
(a) How many full oscillations does the pendulum complete in 1 minute?
(b) How many full oscillations does it complete in 1 hour?
[3 Marks]
(a) How many full oscillations does the pendulum complete in 1 minute?
(b) How many full oscillations does it complete in 1 hour?
✅ Step-by-Step Solution & Working
Pendulum Physics & Math:
• (a) In 1 Minute (60 seconds): Period = 2 seconds. Oscillations = 60 ÷ 2 = 30 oscillations per minute.
• (b) In 1 Hour (3,600 seconds): 3,600 ÷ 2 = 1,800 oscillations per hour.
• (a) In 1 Minute (60 seconds): Period = 2 seconds. Oscillations = 60 ÷ 2 = 30 oscillations per minute.
• (b) In 1 Hour (3,600 seconds): 3,600 ÷ 2 = 1,800 oscillations per hour.
CBSE Step-by-Step Marking Scheme
1 minute = 30 oscillations
1.5 M
1 hour = 1,800 oscillations
1.5 M
Q11
Flight Travel across Time Zones
A flight takes off from Delhi (IST) at 2:30 PM and lands in Dubai at 4:45 PM local time. Dubai time is 1 hour 30 minutes behind Indian Standard Time.
(a) What was the departure time in Dubai local time?
(b) What was the actual flight duration in hours and minutes?
[3 Marks]
(a) What was the departure time in Dubai local time?
(b) What was the actual flight duration in hours and minutes?
✅ Step-by-Step Solution & Working
Time Zone Navigation:
• (a) Departure in Dubai Time: 2:30 PM IST - 1 h 30 min = 1:00 PM Dubai time.
• (b) Actual Flight Duration:
- Both in Dubai time: 1:00 PM to 4:45 PM = 3 hours 45 minutes.
(Check in IST: Lands at 4:45 PM + 1:30 = 6:15 PM IST. 2:30 PM to 6:15 PM = 3 h 45 min).
• (a) Departure in Dubai Time: 2:30 PM IST - 1 h 30 min = 1:00 PM Dubai time.
• (b) Actual Flight Duration:
- Both in Dubai time: 1:00 PM to 4:45 PM = 3 hours 45 minutes.
(Check in IST: Lands at 4:45 PM + 1:30 = 6:15 PM IST. 2:30 PM to 6:15 PM = 3 h 45 min).
CBSE Step-by-Step Marking Scheme
Departure in Dubai time = 1:00 PM
1.5 M
Flight duration = 3 h 45 min
1.5 M
Q12
Countdown Timer • Fireworks Launch
A New Year celebration countdown clock reads 00:08:45 (8 minutes 45 seconds to midnight).
(a) Express the countdown time entirely in seconds.
(b) What will the timer display after 250 seconds have elapsed?
[3 Marks]
(a) Express the countdown time entirely in seconds.
(b) What will the timer display after 250 seconds have elapsed?
✅ Step-by-Step Solution & Working
Working:
• (a) In Seconds: (8 × 60) + 45 = 480 + 45 = 525 seconds.
• (b) Time Remaining:
- 525 s - 250 s = 275 seconds.
- 275 ÷ 60 = 4 minutes with remainder 35 seconds.
- Timer will read: 00:04:35 (4 minutes 35 seconds).
• (a) In Seconds: (8 × 60) + 45 = 480 + 45 = 525 seconds.
• (b) Time Remaining:
- 525 s - 250 s = 275 seconds.
- 275 ÷ 60 = 4 minutes with remainder 35 seconds.
- Timer will read: 00:04:35 (4 minutes 35 seconds).
CBSE Step-by-Step Marking Scheme
525 seconds total
1.5 M
Remaining: 4 min 35 s
1.5 M
Q13
Speed Calculation • Sprinter Rate
A world-class sprinter runs 200 metres in 20 seconds.
(a) What is his speed in metres per second?
(b) Convert this speed into kilometres per hour ($1\text{ m/s} = 3.6\text{ km/h}$).
[3 Marks]
(a) What is his speed in metres per second?
(b) Convert this speed into kilometres per hour ($1\text{ m/s} = 3.6\text{ km/h}$).
✅ Step-by-Step Solution & Working
Speed Conversions:
• (a) Speed in m/s: Distance ÷ Time = 200 m ÷ 20 s = 10 m/s.
• (b) Speed in km/h: 10 m/s × 3.6 = 36 km/h.
• (a) Speed in m/s: Distance ÷ Time = 200 m ÷ 20 s = 10 m/s.
• (b) Speed in km/h: 10 m/s × 3.6 = 36 km/h.
CBSE Step-by-Step Marking Scheme
Speed = 10 m/s
1.5 M
Speed = 36 km/h
1.5 M
Q14
Swimming Lap Times • Decimal Comparison
In a 50-metre freestyle swimming competition, four swimmers clock:
Swimmer A: 26.45 s, Swimmer B: 25.82 s, Swimmer C: 26.05 s, Swimmer D: 25.90 s.
(a) Who won the race?
(b) Arrange the swimmers in order of finish (1st to 4th).
(c) What was the winning margin between 1st place and 2nd place?
[3 Marks]
Swimmer A: 26.45 s, Swimmer B: 25.82 s, Swimmer C: 26.05 s, Swimmer D: 25.90 s.
(a) Who won the race?
(b) Arrange the swimmers in order of finish (1st to 4th).
(c) What was the winning margin between 1st place and 2nd place?
✅ Step-by-Step Solution & Working
Analysis (Fastest = Smallest Time):
• (a) Winner: Swimmer B with 25.82 seconds.
• (b) Order of Finish:
1st: Swimmer B (25.82 s)
2nd: Swimmer D (25.90 s)
3rd: Swimmer C (26.05 s)
4th: Swimmer A (26.45 s).
• (c) Winning Margin: 25.90 - 25.82 = 0.08 seconds (8 hundredths of a second).
• (a) Winner: Swimmer B with 25.82 seconds.
• (b) Order of Finish:
1st: Swimmer B (25.82 s)
2nd: Swimmer D (25.90 s)
3rd: Swimmer C (26.05 s)
4th: Swimmer A (26.45 s).
• (c) Winning Margin: 25.90 - 25.82 = 0.08 seconds (8 hundredths of a second).
CBSE Step-by-Step Marking Scheme
Winner: Swimmer B
1.0 M
Finish order: B, D, C, A
1.0 M
Winning margin = 0.08 s
1.0 M
Q15
Leap Year & Century Math
(a) How many days are in a normal year and in a leap year?
(b) How many seconds are in one normal 24-hour day?
(c) Is the year 2024 a leap year? What about the year 2026?
[3 Marks]
(b) How many seconds are in one normal 24-hour day?
(c) Is the year 2024 a leap year? What about the year 2026?
✅ Step-by-Step Solution & Working
Calendar Science & Math:
• (a) Days: Normal year = 365 days; Leap year = 366 days.
• (b) Seconds in a Day: 24 hours × 60 min × 60 s = 24 × 3,600 = 86,400 seconds.
• (c) Leap Years:
- 2024 is divisible by 4 (2024 ÷ 4 = 506) → 2024 is a Leap Year.
- 2026 ÷ 4 leaves remainder 2 → 2026 is NOT a leap year (normal year of 365 days).
• (a) Days: Normal year = 365 days; Leap year = 366 days.
• (b) Seconds in a Day: 24 hours × 60 min × 60 s = 24 × 3,600 = 86,400 seconds.
• (c) Leap Years:
- 2024 is divisible by 4 (2024 ÷ 4 = 506) → 2024 is a Leap Year.
- 2026 ÷ 4 leaves remainder 2 → 2026 is NOT a leap year (normal year of 365 days).
CBSE Step-by-Step Marking Scheme
365 and 366 days
1.0 M
86,400 seconds in a day
1.0 M
2024 is leap year, 2026 is not
1.0 M
Q16
Baking Oven Timer • Cooking Schedule
A cake recipe requires baking for 45 minutes at 180°C. If the baker preheats the oven for 10 minutes and puts the cake in at 4:40 PM:
(a) At what time should the cake be taken out of the oven?
(b) If the cake needs 20 minutes to cool before icing, at what time can icing begin?
[3 Marks]
(a) At what time should the cake be taken out of the oven?
(b) If the cake needs 20 minutes to cool before icing, at what time can icing begin?
✅ Step-by-Step Solution & Working
Timeline Working:
• (a) Cake Ready: Baking starts at 4:40 PM. 4:40 PM + 45 min = 5:25 PM.
• (b) Icing Time: 5:25 PM + 20 min cooling = 5:45 PM.
• (a) Cake Ready: Baking starts at 4:40 PM. 4:40 PM + 45 min = 5:25 PM.
• (b) Icing Time: 5:25 PM + 20 min cooling = 5:45 PM.
CBSE Step-by-Step Marking Scheme
Out of oven = 5:25 PM
1.5 M
Icing start = 5:45 PM
1.5 M
Q17
Speed of Sound • Lightning & Thunder
Sound travels through air at approximately 340 metres per second. During a monsoon storm, Rohan sees a lightning flash and hears the thunder 5 seconds later.
(a) How far away was the lightning strike in metres?
(b) Express the distance in kilometres.
[3 Marks]
(a) How far away was the lightning strike in metres?
(b) Express the distance in kilometres.
✅ Step-by-Step Solution & Working
Calculations:
• (a) Distance in Metres: Distance = Speed × Time = 340 m/s × 5 s = 1,700 metres.
• (b) In Kilometres: 1,700 ÷ 1,000 = 1.7 km.
• (a) Distance in Metres: Distance = Speed × Time = 340 m/s × 5 s = 1,700 metres.
• (b) In Kilometres: 1,700 ÷ 1,000 = 1.7 km.
CBSE Step-by-Step Marking Scheme
Distance = 1,700 m
1.5 M
In km = 1.7 km
1.5 M
Q18
Mental Arithmetic • Seconds in Multiples of Minutes
Calculate quickly:
(a) Number of seconds in 12 minutes
(b) Number of seconds in 1.5 hours
(c) Number of minutes in 1 day
[3 Marks]
(a) Number of seconds in 12 minutes
(b) Number of seconds in 1.5 hours
(c) Number of minutes in 1 day
✅ Step-by-Step Solution & Working
Mental Calculations:
• (a) 12 Minutes: 12 × 60 = 720 seconds.
• (b) 1.5 Hours: 1.5 × 3,600 = 5,400 seconds.
• (c) 1 Day (24 Hours): 24 × 60 = 1,440 minutes.
• (a) 12 Minutes: 12 × 60 = 720 seconds.
• (b) 1.5 Hours: 1.5 × 3,600 = 5,400 seconds.
• (c) 1 Day (24 Hours): 24 × 60 = 1,440 minutes.
CBSE Step-by-Step Marking Scheme
Part (a): 720 s
1.0 M
Part (b): 5,400 s
1.0 M
Part (c): 1,440 min
1.0 M
Q19
HOTS • Clock Face Mirror Riddle
A boy looks at an analog clock in a mirror. The reflection appears to show 7:20. What is the real actual time on the clock?
[3 Marks]
✅ Step-by-Step Solution & Working
Mirror Time Formula (Subtract from 11:60 or 12:00):
1. Real time = 11:60 - Mirror time.
2. Real time = 11:60 - 7:20 = 4:40.
3. Verification: At 4:40, the hour hand is between 4 and 5, minute hand is at 8. In the mirror, the hand at 8 reflects to 4 (20 minutes past), and the hand between 4 and 5 reflects to between 7 and 8 (hour 7). Verified: Real time is 4:40.
1. Real time = 11:60 - Mirror time.
2. Real time = 11:60 - 7:20 = 4:40.
3. Verification: At 4:40, the hour hand is between 4 and 5, minute hand is at 8. In the mirror, the hand at 8 reflects to 4 (20 minutes past), and the hand between 4 and 5 reflects to between 7 and 8 (hour 7). Verified: Real time is 4:40.
CBSE Step-by-Step Marking Scheme
Mirror time formula (11:60 - time)
1.5 M
Real time = 4:40 with verification
1.5 M
Q20
Slow & Fast Clocks • Error Rate
A wall clock gains 2 minutes every day. It is set correctly at 12:00 noon on Monday.
(a) What time will the clock display at 12:00 noon on Saturday (5 days later)?
(b) How many days will it take for the clock to be fast by exactly 1 hour?
[3 Marks]
(a) What time will the clock display at 12:00 noon on Saturday (5 days later)?
(b) How many days will it take for the clock to be fast by exactly 1 hour?
✅ Step-by-Step Solution & Working
Error Calculations:
• (a) Saturday Reading:
- Days elapsed = 5 days.
- Total gain = 5 × 2 min = 10 minutes.
- Clock will display: 12:10 PM.
• (b) Days to Gain 1 Hour (60 min): 60 ÷ 2 min/day = 30 days.
• (a) Saturday Reading:
- Days elapsed = 5 days.
- Total gain = 5 × 2 min = 10 minutes.
- Clock will display: 12:10 PM.
• (b) Days to Gain 1 Hour (60 min): 60 ÷ 2 min/day = 30 days.
CBSE Step-by-Step Marking Scheme
Saturday display = 12:10 PM
1.5 M
30 days to gain 1 hour
1.5 M
Q21
Earth Rotation Speed • Astronomy Math
The Earth completes one full rotation of 360° on its axis in 24 hours.
(a) Through how many degrees does the Earth rotate in 1 hour?
(b) How many minutes does the Earth take to rotate through 1 degree?
[3 Marks]
(a) Through how many degrees does the Earth rotate in 1 hour?
(b) How many minutes does the Earth take to rotate through 1 degree?
✅ Step-by-Step Solution & Working
Planetary Rotation Math:
• (a) Degrees per Hour: 360° ÷ 24 h = 15° per hour.
• (b) Time per Degree: 1 hour = 60 minutes. Time for 1° = 60 min ÷ 15° = 4 minutes per degree.
• (a) Degrees per Hour: 360° ÷ 24 h = 15° per hour.
• (b) Time per Degree: 1 hour = 60 minutes. Time for 1° = 60 min ÷ 15° = 4 minutes per degree.
CBSE Step-by-Step Marking Scheme
15° per hour
1.5 M
4 minutes per degree
1.5 M
Q22
Heartbeat vs Breath Ratio
A sleeping child takes 20 breaths per minute, while her heart beats 80 times per minute.
(a) Find the ratio of heartbeats to breaths in simplest form.
(b) How many heartbeats occur during 1 single breath?
[3 Marks]
(a) Find the ratio of heartbeats to breaths in simplest form.
(b) How many heartbeats occur during 1 single breath?
✅ Step-by-Step Solution & Working
Ratio & Unit Rate:
• (a) Ratio: Heartbeats : Breaths = 80 : 20 = 4 : 1.
• (b) Heartbeats per Breath: 80 ÷ 20 = 4 heartbeats per breath.
• (a) Ratio: Heartbeats : Breaths = 80 : 20 = 4 : 1.
• (b) Heartbeats per Breath: 80 ÷ 20 = 4 heartbeats per breath.
CBSE Step-by-Step Marking Scheme
Ratio = 4 : 1
1.5 M
4 heartbeats per breath
1.5 M
Q23
True or False with Time Reasoning
State True or False with reasoning:
(a) 2.5 hours means 2 hours 50 minutes.
(b) Midnight in 24-hour time can be written as 00:00 or 24:00.
(c) A leap century year like 2000 is divisible by 400.
[3 Marks]
(a) 2.5 hours means 2 hours 50 minutes.
(b) Midnight in 24-hour time can be written as 00:00 or 24:00.
(c) A leap century year like 2000 is divisible by 400.
✅ Step-by-Step Solution & Working
Justifications:
• (a) False: 0.5 hour = half of 60 minutes = 30 minutes. Therefore 2.5 hours is 2 hours 30 minutes, not 2 hours 50 minutes.
• (b) True: 00:00 represents the beginning of the day, and 24:00 represents the conclusion of the day.
• (c) True: For century years ending in '00', a year is only a leap year if it is divisible by 400 (e.g. 2000 was a leap year, but 1900 was not).
• (a) False: 0.5 hour = half of 60 minutes = 30 minutes. Therefore 2.5 hours is 2 hours 30 minutes, not 2 hours 50 minutes.
• (b) True: 00:00 represents the beginning of the day, and 24:00 represents the conclusion of the day.
• (c) True: For century years ending in '00', a year is only a leap year if it is divisible by 400 (e.g. 2000 was a leap year, but 1900 was not).
CBSE Step-by-Step Marking Scheme
Part (a): False (2.5 h = 2 h 30 min)
1.0 M
Part (b): True with 24-hour explanation
1.0 M
Part (c): True with century leap rule
1.0 M
Q24
Comprehensive Time Mastery Review
An astronaut on the International Space Station orbits the Earth once every 90 minutes.
(a) How many orbits does the space station complete in one 24-hour day?
(b) How many sunrises and sunsets do the astronauts experience in a day?
[3 Marks]
(a) How many orbits does the space station complete in one 24-hour day?
(b) How many sunrises and sunsets do the astronauts experience in a day?
✅ Step-by-Step Solution & Working
Orbital Time Calculations:
• (a) Orbits in 24 Hours:
- 24 hours = 24 × 60 = 1,440 minutes.
- Orbits = 1,440 ÷ 90 = 16 orbits per day.
• (b) Sunrises & Sunsets: Each orbit brings 1 sunrise and 1 sunset. In 16 orbits, the astronauts witness 16 sunrises and 16 sunsets every single day!
• (a) Orbits in 24 Hours:
- 24 hours = 24 × 60 = 1,440 minutes.
- Orbits = 1,440 ÷ 90 = 16 orbits per day.
• (b) Sunrises & Sunsets: Each orbit brings 1 sunrise and 1 sunset. In 16 orbits, the astronauts witness 16 sunrises and 16 sunsets every single day!
CBSE Step-by-Step Marking Scheme
Total day = 1,440 minutes
1.0 M
Orbits = 16
1.0 M
16 sunrises and 16 sunsets
1.0 M
🌟 NEP 2020 Competency-Based Case Study
Competency Question: Intercity Vande Bharat Express Timetable
The Vande Bharat Express departs New Delhi station at 06:00 hours and arrives at Varanasi Junction at 14:00 hours, covering a rail distance of 759 km.
Analytical Task: (a) What is the total travel duration of the train in hours?
(b) What is the average speed of the train in km/h?
(b) What is the average speed of the train in km/h?
Evaluation & Model Answer:
Suggested Model Solution:
(a) Duration: 14:00 - 06:00 = 8 hours.
(b) Average Speed: 759/8 = 94.875 km/h.
Rubric: 1M concept identification + 1M step execution + 1M conclusion