at 32/11 min. past 4.

at 32/11 min. past 4.

at 35/11 min. past 4.

at 40/11 min. past 4.

D. at 40/11 min. past 4.

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 minute spaces. 55 min. spaces are gained by it in 60 min.

5 min spaces will be gained by it in __60*5/55 __ min=60/11min.

:. They are at right angles at 60/11min. past 4.

Case II. When the minute hand is 15 min. spaces *ahead *of the *hour *hand:

To be in this position, the minute hand will have to gain (20 + 15) = 35 minute spa' 55 min. spaces are gained in 60 min.

35 min spaces are gained in (__60 __x 35)/55 min =40/11