varunmaheshwari wrote:
Karishma,
Shouldn't this question be like what will the maximum / minimum time was Mr A away from home, considering that we are going to have 2 possibilities.
Also, how can we solve this types of ques.
Yes, if you want to make it a PS question, you can definitely ask for the maximum or minimum time. There are going to be 4 possibilities (2C1 * 2C1). 2 possibilities for the time at which he leaves. 2 possibilities for the time at which he returns.
How to solve it?
Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is 45 degrees. He returns between 6 and 7 pm same day and notices that the angle is again 45 degrees. What is the minimum time for which Mr A was away from home?
Let's focus on the minimum time that he was away. For that he should have left later and arrived earlier. So he should have left at around 3:25 and arrived at around 6:25 (Look at the diagram above to see the case we are talking about)
At 3 o clock, the angle between the hour and minute hand is 90 degrees.
The minute hand should cover the 90 degrees and then create an angle of 45 degrees between itself and the hour hand.
Relative speed of minute hand is 330 degrees/hour.
To cover 135 degrees relative to the hour hand, it will take 60/330 * 135 minutes = 270/11 minutes = 24(6/11) minutes
He must have left at 24(6/11) minutes past 3.
At 6 o clock, the angle between the hour and minute hand is 180 degrees.
The minute hand should cover 135 degrees relative to the hour hand to create an angle of 45 degrees.
This is because 180-45 = 135 degrees and not 90+45 degrees - Highlighted to see that evryone gets the reason. Anyway it will become clear in the Maximum exampleRelative speed of minute hand is 330 degrees/hour.
To cover 135 degrees relative to the hour hand, it will take 60/330 * 135 minutes = 270/11 minutes = 24(6/11) minutes.
He must have arrived at 24(6/11) minutes past 6.
This means he was out for exactly 3 hours.
Now try the case of 'maximum time' and put it up.
Mr. A leaves his house between 3 and 4 pm and notices that the angle between the hour and minute hands is 45 degrees. He returns between 6 and 7 pm same day and notices that the angle is again 45 degrees. What is the maximum time for which Mr A was away from home?