In (a), counting from 6:00 am to 10:00 am gives 4 hours, plus 30 minutes gives 4 hours 30 minutes. In (b), both times share 45 minutes; from 8 am to 12 pm is 4 hours. In (c), from 9:30 pm to 12:00 midnight is 2 hours 30 minutes, and to 1:30 am is another 1 hour 30 minutes, giving 4 hours. In (d), from 1:30 am to 11:30 am is 10 hours, plus 15 minutes gives 10 hours 15 minutes.

In (a), counting from 6:00 am to 10:00 am gives 4 hours, plus 30 minutes gives 4 hours 30 minutes. In (b), both times share 45 minutes; from 8 am to 12 pm is 4 hours. In (c), from 9:30 pm to 12:00 midnight is 2 hours 30 minutes, and to 1:30 am is another 1 hour 30 minutes, giving 4 hours. In (d), from 1:30 am to 11:30 am is 10 hours, plus 15 minutes gives 10 hours 15 minutes.

For Question 2, split at 12:00 noon: from 10:30 am to 12:00 noon is 1 hour 30 minutes, and from noon to 5:00 pm is 5 hours. Adding these gives 6 hours 30 minutes. For Question 3, from 8:15 am to 12:00 noon is 3 hours 45 minutes, and noon to 2:30 pm is 2 hours 30 minutes. Adding them gives 5 hours 75 minutes, which simplifies to 6 hours 15 minutes.

For Question 2, split at 12:00 noon: from 10:30 am to 12:00 noon is 1 hour 30 minutes, and from noon to 5:00 pm is 5 hours. Adding these gives 6 hours 30 minutes. For Question 3, from 8:15 am to 12:00 noon is 3 hours 45 minutes, and noon to 2:30 pm is 2 hours 30 minutes. Adding them gives 5 hours 75 minutes, which simplifies to 6 hours 15 minutes.

For Question 4, from 6:25 am to 12:25 pm is exactly 6 hours, and from 12:25 pm to 12:30 pm is 5 minutes, making the total travel time 6 hours 5 minutes. For Question 5, from 3:30 pm to 4:30 pm is 1 hour, and from 4:30 pm to 5:18 pm is 48 minutes, giving a total of 1 hour 48 minutes.

For Question 4, from 6:25 am to 12:25 pm is exactly 6 hours, and from 12:25 pm to 12:30 pm is 5 minutes, making the total travel time 6 hours 5 minutes. For Question 5, from 3:30 pm to 4:30 pm is 1 hour, and from 4:30 pm to 5:18 pm is 48 minutes, giving a total of 1 hour 48 minutes.

For Question 6, add 36 minutes to 15 minutes past 2: 15 + 36 = 51, so Ishani reaches her stop at 2:51 pm. For Question 7, Ashwin took less time (1 min 20 s) compared to Anand (1 min 31 s), which means Ashwin ran faster. The difference is 31 - 20 = 11 seconds.

For Question 6, add 36 minutes to 15 minutes past 2: 15 + 36 = 51, so Ishani reaches her stop at 2:51 pm. For Question 7, Ashwin took less time (1 min 20 s) compared to Anand (1 min 31 s), which means Ashwin ran faster. The difference is 31 - 20 = 11 seconds.

For Question 8, adding the minutes: 56 + 21 = 77 minutes = 1 hour 17 minutes. Adding this to the 1 hour already there gives 2 hours 17 minutes. For Question 9, add the seconds: 15 + 10 + 18 = 43 seconds. Then add the minutes: 12 + 9 + 16 = 37 minutes. The total speaking time is 37 minutes 43 seconds.

For Question 8, adding the minutes: 56 + 21 = 77 minutes = 1 hour 17 minutes. Adding this to the 1 hour already there gives 2 hours 17 minutes. For Question 9, add the seconds: 15 + 10 + 18 = 43 seconds. Then add the minutes: 12 + 9 + 16 = 37 minutes. The total speaking time is 37 minutes 43 seconds.

Exercise 10.5 1. Calculate the time duration: (a) From $6\text{ am}$ to $10:30\text{ am}$ (b) From $8:45\text{ am}$ to $12:45\text{ pm}$ (c) From $9:30\text{ pm}$ to $1:30\text{ am}$ (d) From $1:30\text{ am}$ to $11:45\text{ am}$ 2. Father works in his office from $10:30\text{ am}$ to $5\text{ pm}$ . Calculate the time he spends in office? 3. A bank opens at $8:15\text{ am}$ and closes at $2:30\text{ pm}$ . How long does the bank remain open? 4. A train started at $6:25\text{ am}$ and reached its destination at $12:30\text{ pm}$ . Find the total time taken by the train. 5. A flight took off at $3:30\text{ pm}$ from Delhi and reached Hyderabad at $5:18\text{ pm}$ . Find the time taken by the flight. 6. A school bus leaves school at $2:15\text{ pm}$ and takes $36\text{ minutes}$ to reach Ishani's bus-stop. At what time does Ishani reach her bus-stop? 7. In a race, Ashwin's timing was recorded as $1\text{ minute } 20\text{ seconds}$ and Anand's timing was recorded as $1\text{ minute } 31\text{ seconds}$ . Who ran faster? By how much time was the winner ahead? 8. Sameer played tennis for $56\text{ minutes}$ and football for $1\text{ hour } 21\text{ minutes}$ . For how long did he play? 9. Rashi spoke to Raju for $12\text{ minutes } 15\text{ seconds}$ ; to Pradip, for $9\text{ minutes } 10\text{ seconds}$ ; and to Seema for $16\text{ minutes } 18\text{ sec}$ from her mobile. What was the total time she spent talking on her mobile?

Answer: 1. (a) 4 hours 30 minutes, (b) 4 hours, (c) 4 hours, (d) 10 hours 15 minutes; 2. 6 hours 30 minutes; 3. 6 hours 15 minutes; 4. 6 hours 5 minutes; 5. 1 hour 48 minutes; 6. 2:51 pm; 7. Ashwin ran faster by 11 seconds; 8. 2 hours 17 minutes; 9. 37 minutes 43 seconds.

Step-by-step solution

Step 1: Calculate durations for Question 1

In (a), counting from $6:00\text{ am}$ to $10:00\text{ am}$ gives $4$ hours, plus $30$ minutes gives $4\text{ hours } 30\text{ minutes}$ . In (b), both times share $45$ minutes; from $8\text{ am}$ to $12\text{ pm}$ is $4\text{ hours}$ . In (c), from $9:30\text{ pm}$ to $12:00\text{ midnight}$ is $2\text{ hours } 30\text{ minutes}$ , and to $1:30\text{ am}$ is another $1\text{ hour } 30\text{ minutes}$ , giving $4\text{ hours}$ . In (d), from $1:30\text{ am}$ to $11:30\text{ am}$ is $10$ hours, plus $15$ minutes gives $10\text{ hours } 15\text{ minutes}$ .

Step 2: Solve Questions 2 and 3

For Question 2, split at 12:00 noon: from $10:30\text{ am}$ to $12:00\text{ noon}$ is $1\text{ hour } 30\text{ minutes}$ , and from noon to $5:00\text{ pm}$ is $5\text{ hours}$ . Adding these gives $6\text{ hours } 30\text{ minutes}$ . For Question 3, from $8:15\text{ am}$ to $12:00\text{ noon}$ is $3\text{ hours } 45\text{ minutes}$ , and noon to $2:30\text{ pm}$ is $2\text{ hours } 30\text{ minutes}$ . Adding them gives $5\text{ hours } 75\text{ minutes}$ , which simplifies to $6\text{ hours } 15\text{ minutes}$ .

Step 3: Solve Questions 4 and 5

For Question 4, from $6:25\text{ am}$ to $12:25\text{ pm}$ is exactly $6\text{ hours}$ , and from $12:25\text{ pm}$ to $12:30\text{ pm}$ is $5\text{ minutes}$ , making the total travel time $6\text{ hours } 5\text{ minutes}$ . For Question 5, from $3:30\text{ pm}$ to $4:30\text{ pm}$ is $1\text{ hour}$ , and from $4:30\text{ pm}$ to $5:18\text{ pm}$ is $48\text{ minutes}$ , giving a total of $1\text{ hour } 48\text{ minutes}$ .

Step 4: Solve Questions 6 and 7

For Question 6, add $36$ minutes to $15$ minutes past $2$ : $15 + 36 = 51$ , so Ishani reaches her stop at $2:51\text{ pm}$ . For Question 7, Ashwin took less time ( $1\text{ min } 20\text{ s}$ ) compared to Anand ( $1\text{ min } 31\text{ s}$ ), which means Ashwin ran faster. The difference is $31 - 20 = 11\text{ seconds}$ .

Step 5: Solve Questions 8 and 9

For Question 8, adding the minutes: $56 + 21 = 77\text{ minutes} = 1\text{ hour } 17\text{ minutes}$ . Adding this to the $1\text{ hour}$ already there gives $2\text{ hours } 17\text{ minutes}$ . For Question 9, add the seconds: $15 + 10 + 18 = 43\text{ seconds}$ . Then add the minutes: $12 + 9 + 16 = 37\text{ minutes}$ . The total speaking time is $37\text{ minutes } 43\text{ seconds}$ .

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