Kapil leaves his house 20 minutes before six in the morning, reaching Kamal's house in 25 minutes. They finish their breakfast in another 15 minutes…

Kapil leaves his house 20 minutes before six in the morning.

Six in the morning is 6:00 AM.

20 minutes before 6:00 AM is 5:40 AM.

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Kapil travels for 25 minutes to reach Kamal's house.

Time of departure: 5:40 AM

Travel time: 25 minutes

Time of arrival at Kamal's house:

$$5:40 \text{ AM} + 25 \text{ minutes}$$5:40 AM+25 minutes

$$= 6:05 \text{ AM}$$=6:05 AM

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They finish their breakfast in 15 minutes.

Breakfast starts at: 6:05 AM

Breakfast duration: 15 minutes

Breakfast ends at:

$$6:05 \text{ AM} + 15 \text{ minutes}$$6:05 AM+15 minutes

$$= 6:20 \text{ AM}$$=6:20 AM

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They leave for their institute immediately after finishing breakfast.

Therefore, they leave Kamal's house at 6:20 AM.

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Answer: 6:20 AM (as per answer key)