A man drove his car northward,then turned left and drove 10 km and again turned left and drove 20 km.He found himself 10 km west of his starting point.How far did he drive northward initially.

Answer 1

make a simple sketch , to see that he completed a rectangle, so he must have traveled 20 km north

or, suppose you don't see that right away:

label his trips, AB, then BC, then BD
from D draw a horizontal to meet AB at E
so in right-angled triangle AED,
AE^2 + 10^2 = 10^2
AE = 0