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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.

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  • $\begingroup$ what do you mean, "at the next four minutes"? In four minutes? $\endgroup$ – sousben Oct 3 '17 at 11:06
  • $\begingroup$ @sousben The phrase "at the next four minutes" means four minutes from the current time. $\endgroup$ – James Oct 3 '17 at 11:17
  • $\begingroup$ does the question mean that the hands of the clocks are in right angle currently? $\endgroup$ – sousben Oct 3 '17 at 11:19
  • $\begingroup$ @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 $\endgroup$ – James Oct 3 '17 at 11:23
  • $\begingroup$ how does this answer my question? $\endgroup$ – sousben Oct 3 '17 at 11:26
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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

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    $\begingroup$ On a 12-hour watch, I don't think it could be 15:31. $\endgroup$ – D Krueger Oct 3 '17 at 12:57
  • $\begingroup$ @DKrueger why not? the next right angle is only at 15:32 $\endgroup$ – sousben Oct 3 '17 at 13:06
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    $\begingroup$ Because on a 12-hour watch, there is no 15. ;) $\endgroup$ – D Krueger Oct 3 '17 at 13:13
  • $\begingroup$ 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. :) $\endgroup$ – Cockabondy Oct 3 '17 at 15:04

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