Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

We need to calculate the distance, then we can calculate the time and finally our answer.
Lets solve this,
Let the distance travelled by x km
Time = Distance/Speed
$\frac{x}{10}-\frac{x}{15}=2$
$(because, 2 pm - 12 noon = 2 hours)$
$3x-2x=60 \therefore x=60.$
$Time=\frac{Dis\tan ce}{Speed}$
$Time@10km/hr=\frac{60}{10}=6hours$
So 2 P.M. - 6 = 8 A.M
Robert starts at 8 A.M.
He have to reach at 1 P.M. i.e, in 5 hours
So, Speed = 60/5 = 12 km/hr