It should be:


  Today I met an old colleague on the way to work.


And, for the question:


  Who did I meet on the way to work today?


It's did and not do because it is in the past tense. You aren't currently meeting the colleague on the way to work. Also, because it is the verb to do, the verb to meet stays in present tense because do, along with be and have, is a primary auxiliary verb.

Edit: I'm assuming you aren't talking about your escapades in daily life as if they were a story. If you were, it would be Who do I meet on the way to work today? because narratives are recounted in the present tense. But since you shouldn't talk about your day in normal conversation like it's part of a story, you should use the past tense.

Who did/do I met today on the way to work?
The $ABCD$ paralelograms sides are $AB,BC,CD,DA$. On these line segments there are points in the same order: $X,Y,Z,V$. We know, that: $$\frac{AX}{XB}=\frac{BY}{YC}=\frac{CZ}{ZD}=\frac{DV}{VA}=k$$

$k$ is a positive constant what is less then $\frac{1}{2}$. What is the value of $k$, if the area of $XYZV$ is 86% of the area of $ABCD$?

Can you tell me a step by step answer to this question?
