Distance and Direction Formulas, Shortcuts, Tips and Tricks

One Man Problem

In this problem, only one man is there in the system and he is moving left right or north west, east, south etc.

Example – A man starts from a point ‘X’ and walks 3 km southwards, then he turns left and walks 6 km. In which direction is he from the starting point?

Two Men Problem

In most of the questions, from the starting point there is only 1 object in motion(changing directions and distance). However, in two man problems, there are two independent objects moving.

Ways to solve 2 man problem

Let us look at an example to solve this –

Siddharth and Murali go for jogging from the same point. Siddharth goes towards the east covering 4 km. Murali proceeds towards the west for 3 km. Siddharth tuns left and covers 4 km and Murali turns to the right to cover 1 km. Now what will be the distance between Siddharth and Murali?

First we should draw the diagram which will look like this –

Now you can use Pythagoras theorem to solve this questions or use Cheat Scale method.(If you don’t know cheat scale method check here)

With cheat scale method the answer comes out to be between 7.6 and 7.7.

With Pythagoras method answer will be

Ans = root((3+4)² + (4-1)²)

Degree based problems

Sunil was facing east. He turns 150 o in the clockwise direction and then 145 o in the anticlockwise direction. Which direction is he facing now?

The person simultaneously turns 150 degrees clockwise and then turns 145 degrees anti-clockwise, thus his total movement will only be 5 degrees clockwise.

Thus, if he was facing easy he moved 5 degrees towards south side. Thus, his direction will be South east. More of east less of south