Determine the current time

When ten-year-old Rohan wanted to know the current time, his uncle Rakesh looked at his 12-hour analog wristwatch, and replied:

“In four minutes, it will be exactly ten times as many seconds past the half-hour as it was minutes before the same half-hour the last time the two hands were at a right angle this afternoon.”

Determine the current time, assuming that the above conversation took place after 12:00 P.M. but before 12:00 A.M.

• what do you mean, "at the next four minutes"? In four minutes? Oct 3, 2017 at 11:06
• @sousben The phrase "at the next four minutes" means four minutes from the current time. Oct 3, 2017 at 11:17
• does the question mean that the hands of the clocks are in right angle currently? Oct 3, 2017 at 11:19
• @sousben The time when the two hands were in right angles, the hour hand and the minute hand were precisely situated on two distinct minute marks Oct 3, 2017 at 11:23
• how does this answer my question? Oct 3, 2017 at 11:26

It could be

15:31 The last 90deg was at 15:00, 30 min before the second half of the hour. In 4 minutes it will be 15:35, 300s after the second half of the hour

or

13:27:30 (rounding the fractions of second). The last 90deg was at 13:21 that is 9 minutes before the second half hour. In 4 minutes it will be 1:31:30 which is 90s after the second half hour

or many other possible solutions...

The question seems to imply a unique answer so I may not have understood it well

• On a 12-hour watch, I don't think it could be 15:31. Oct 3, 2017 at 12:57
• @DKrueger why not? the next right angle is only at 15:32 Oct 3, 2017 at 13:06
• Because on a 12-hour watch, there is no 15. ;) Oct 3, 2017 at 13:13
• I think your answer fits well for the specified conditions, just maybe do time corrections, and add all possibilities which you also saw. *just to note, afternoon might be only till 4/6/8p.m. But should be not later. :) Oct 3, 2017 at 15:04