Ticking Clocks and Turning Calendar — NCERT Solutions

Note: This is a research/exploration activity.

Sample Answer (Hindu Calendar months and approximate English months):

Students should explore the calendar of their own community and make a similar comparison.

Note: This is a research/exploration activity.

Sample Answer:

• Diwali falls in the Hindu month of Kartika (Amavasya — new moon night).
• Holi falls in the Hindu month of Phalguna (Purnima — full moon night).
• Eid-ul-Fitr falls at the end of the Islamic month of Ramadan.
• Guru Nanak Jayanti falls in the Sikh/Hindu month of Kartika (Purnima).

Students should identify festivals from their own community's calendar.

Note: This is an observation-based exploration activity.

Concept: In the Hindu and Islamic calendars, months are based on the lunar cycle.

Pattern observed:

• The full moon (Purnima) falls on the 15th day of every lunar month.
• The new moon (Amavasya) falls on the last day (30th or 29th) of every lunar month.
• The lunar cycle repeats approximately every 29–30 days.
• So the new moon and full moon occur roughly once every month, about 15 days apart from each other.

Students should check their community's calendar and verify this pattern.

Note: This is a research/exploration activity.

Sample Answer:

• In the Hindu calendar, the full moon day is called Purnima and the new moon day is called Amavasya.
• In the Islamic calendar, the new moon marks the beginning of each new month (e.g., the sighting of the crescent moon marks the start of Ramadan or Eid).
• In the Sikh tradition, the full moon day is called Puranmashi and the new moon day is called Masya.

Students should find out the specific names used in their own community's calendar.

Given: A table showing times in AM/PM format and 24-hour digital clock format.

Concept:

• AM times (12:00 AM to 11:59 AM): 12:00 AM = 00:00 hours; 1:00 AM = 01:00 hours, and so on up to 11:59 AM = 11:59 hours.
• PM times (12:00 PM to 11:59 PM): 12:00 PM = 12:00 hours; 1:00 PM = 13:00 hours; add 12 to the hour for 1 PM onwards.

Working:

1. 9:45 AM → 9:45 hours (AM times before noon stay the same)

$$\text{Answer: } 9:45 \text{ hours}$$

2. 11:20 hours → This is before 12:00 noon, so it is AM.

$$\text{Answer: } 11:20 \text{ AM}$$

3. 3:00 PM → $3 + 12 = 15$

$$\text{Answer: } 15:00 \text{ hours}$$

4. 5:20 PM → $5 + 12 = 17$

$$\text{Answer: } 17:20 \text{ hours}$$

5. 20:00 hours → $20 - 12 = 8$, and since it is after 12 noon, it is PM.

$$\text{Answer: } 8:00 \text{ PM}$$

Complete Table:

Given: Raghav leaves at 8:20 AM and returns at 8:35 AM.

Concept: Time taken = Return time − Departure time.

Working:
$$8:35 - 8:20 = 15 \text{ minutes}$$

Answer: Raghav has taken 15 minutes.

Given: Start time = 10:20 AM; Time taken = 25 minutes.

Concept: Finish time = Start time + Time taken.

Working:
$$10:20 + 25 \text{ minutes} = 10:45 \text{ AM}$$
(Since $20 + 25 = 45$ minutes, and $45 < 60$, the hour does not change.)

Answer: Raghav finished his homework at 10:45 AM.

The clock should show the minute hand pointing to 9 (45 minutes) and the hour hand between 10 and 11.

Given: Start time = 4:15 PM; Time taken = 45 minutes.

Concept: Finish time = Start time + Time taken.

Working:
$$4:15 + 45 \text{ minutes}$$
$$= 4 \text{ hours } (15 + 45) \text{ minutes}$$
$$= 4 \text{ hours } 60 \text{ minutes}$$
$$= 4 \text{ hours} + 1 \text{ hour} = 5:00 \text{ PM}$$
(Since $15 + 45 = 60$ minutes $= 1$ hour exactly.)

Answer: Muneera finished reading at 5:00 PM.

The clock should show the minute hand pointing to 12 (0 minutes) and the hour hand pointing to 5.

Given: Akira leaves at 8:00 AM; she takes 15 minutes to reach school.

Concept: Finish time = Start time + Time taken; 1 hour = 60 minutes.

Working:
$$8:00 + 15 \text{ minutes} = 8:15 \text{ AM}$$

Relation between 1 hour and 60 minutes:
$$1 \text{ hour} = 60 \text{ minutes}$$
So half an hour $= 30$ minutes, and a quarter hour $= 15$ minutes.

Answer: Akira reaches school at 8:15 AM.

The clock should show the minute hand pointing to 3 (15 minutes) and the hour hand slightly past 8.

Concept: On an analogue clock:

• The short (hour) hand points to the hour.
• The long (minute) hand points to the minutes. Each number on the clock represents 5 minutes (e.g., the hand pointing to 1 = 5 minutes, pointing to 2 = 10 minutes, pointing to 4 = 20 minutes, pointing to 7 = 35 minutes).

Analysis of each clock:

Clock 1:

• Raghu reads 12:04 — He is reading the minute hand position as the number 4 itself (confusing the number with the minutes). This is wrong.
• Raghav reads 12:20 — The minute hand is on 4, so $4 \times 5 = 20$ minutes. Hour hand is on 12. This is correct.
• Rani reads 04:00 — She is reading the minute hand as the hour. This is wrong.

Clock 2:

• Raghu reads 07:07 — He is reading the minute hand number (7) directly as minutes. This is wrong.
• Raghav reads 07:25 — The minute hand is on 5, so $5 \times 5 = 25$ minutes. Hour hand is on 7. This is correct.
• Rani reads 05:35 — She is reading the minute hand as the hour and multiplying the hour hand. This is wrong.

Clock 3:

• Raghu reads 03:07 — He is reading the minute hand number (7) directly as minutes. This is wrong.
• Raghav reads 03:35 — The minute hand is on 7, so $7 \times 5 = 35$ minutes. Hour hand is on 3. This is correct.
• Rani reads 07:15 — She is reading the minute hand as the hour. This is wrong.

Answer: Raghav is correct in all three cases.

How to read a clock correctly:

1. Look at the short (hour) hand — it tells the hour.
2. Look at the long (minute) hand — multiply the number it points to by 5 to get the minutes.
3. Write the time as Hour : Minutes.

For example, if the hour hand is on 3 and the minute hand is on 7: Time $= 3$ hours and $7 \times 5 = 35$ minutes $=$ 3:35.