A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?

Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours. 

24 hours 10 min. of this clock = 24 hours of the correct clock. 

$\frac{145}{6}$ hrs of this clock = 24 hours of the correct clock. 

29 hours of this clock =  $24*\frac{6}{145}*29$ hrs of the correct clock 

= 28 hrs 48 min of the correct clock. 

Therefore, the correct time is 28 hrs 48 min. after 8 a.m. 

This is 48 min. past 12.