Time

parallel_chase wrote:Approximately at what time after 2 PM, the hour hand and the minute hand of a clock forms a right angle?

A. 3:00
B. 2:40
C. 2:27
D. 3:30
E. 2:05

OA after few discussions.

IMO its D. 2:27

in a clock the hours and minutes hand should be 15 minutes apart to be @ right angle

@2'clock the difference between the 2 hands is 10 minutes.
In 60 minutes , the minutes hand gain 55 minutes on the hour hand..

when the minute hand is 15 spaces from the original.. the position of the minutes hand should be @ 10 + 15 mints

thus 25 minutes spaces between them will be @

60/55*25=27 minutes...

Hope its clear

02:27

I still don't get it. Why is it D? I get the bit where the hour and minute hand should be 15 mins apart for a right angle to be formed between them but I just don't get how 2:27 satisfies that. Any input will be highly appreciated.

The method posted by sudhir is absolutely right.

Here is another method:

Minute hand moves 360 degrees in 1 hour
Therefore it moves = 360/60 = 6 degrees per minute

Hour hand moves 360 degree in 12 hour
Therefore it moves = 360/12 = 30 degrees per hour & 30/60 = 1/2 degrees per minute.

at 2 O'clock minute hand will be 10 minutes behind hour hand or 60 degrees behind minute hand.

We want both the hands to form a 90 degrees angle after 2 o'clock.

The minute hand will cover more distance as compared to hour hand

Therefore, 60+90 = 150 degrees

The increasing or decreasing distance between both the hand is 6-1/2 = 5.5 degrees

5.5x = 150
x = 1500/55 = 300/11 =27.27 minutes

Hence the answer is 2:27

Let me know if you have any doubts.

Here is another approach

eliminate E & B &D as obvious

A would be an easy choice. But we have to validate 2.27

1) The minute hand is at an agnle of 27/30*180 from 12 (27 minutes past the hour ... 30 is the 180 degree mark)
2) The hour hand is (147/360)*180 from 12. (360 is 60 minutes *60 hours ... 147 is 2 hours and 27 minutes)

1) equals 162 degrees
2) equals 73.5 degrees

1) - 2) = 88.5 degrees

The question asks for approximately. I'd be hardpressed during the exam to take a leap from 88.5 to 90. But for lack of better this will have to do.

Thanks parallel_chase. That totally made sense!!

I am confused: is it D or C?