Question

How many times between 4 a.m. and 5 a.m. the minute and hour hands of a clock will be at right angles?

• A. $2$
• B. $3$
• C. $4$
• D. $1$

Answer 1

The correct option is A $2$

At 4 O' clock, the minute hand will be 20 min. spaces behind the hour hand.
Now, when the two hands are at right angles, they are 15 min spaces apart.
So, they are at right angles in following two cases.
Case I :
When minute hand is 15 min. spaces behind the hour hand :
In this case min. hand will have to gain (20-15)=5 min. spaces 55 min. spaces are gained by it in 60 min.
5 min. spaces will be gained by it in (6055×5)min.Unknown node type: g6055×5)minUnknown node type: gUnknown node type: g6055×5)minUnknown node type: g past 4.