10. In my office there are two digital 24-hour clocks. One clock gains one minute every hour and the other loses two minutes every hour. Yesterday I set both of them to the same time but when I looked at them today, I saw that the time shown on one was 11:00 and the time on the other was 12:00.
What time was it when I set the two clocks?
A 23:00
B $19: 40$
C 15:40
D 14:00
E 11:20
SolUTION
$\mathbf{C}$

Since one clock gains one minute each hour and the other clock loses two minutes each hour, for each hour that passes the difference between the times shown by the two clocks increases by three minutes. Therefore the amount of time in hours that has passed since the clocks were set is $60 \div 3=20$. In 20 hours, the clock that gains time will have gained 20 minutes. Hence the time at which the clocks were set is 20 hours and 20 minutes before $12: 00$ and so is $15: 40$.