A child walked 90 m towards the East to look for his father, then turned right and walked 20 m. After this, he turned right again and, after walking 30 m, reached his uncle's house. Not finding his father there, he walked 100 m towards the North and met his father. How far from the starting point did he meet his father?

Introduction:
This problem describes a series of movements by a child who first walks East, then makes two right turns to reach his uncle's house, and finally walks North to meet his father. We are asked to find the straight-line distance from the starting point to the place where he meets his father. A coordinate geometry approach makes it straightforward to track his movements and compute the final distance.

Given Data / Assumptions:
• The child first walks 90 m towards the East.• He then turns right and walks 20 m.• He turns right again and walks 30 m to reach his uncle's house.• From his uncle's house, he walks 100 m towards the North and meets his father.• We assume level ground and usual interpretations of right turn and cardinal directions.

Concept / Approach:
We treat his path as movement on an x–y coordinate grid, with East as positive x, West as negative x, North as positive y and South as negative y. Each right turn is a 90 degree clockwise rotation from his current facing direction. By updating both position and facing direction, we can compute his final coordinates relative to the starting point. The straight-line distance is then found using the Pythagorean theorem.

Step-by-Step Solution:
Step 1: Place the starting point at (0, 0) with the child initially facing East. Walking 90 m East moves him to (90, 0).Step 2: From East, a right turn makes him face South. Walking 20 m South takes him to (90, −20).Step 3: From South, another right turn makes him face West. Walking 30 m West from (90, −20) moves him to (60, −20). This is his uncle's house.Step 4: From the uncle's house, he walks 100 m towards the North. That increases the y-coordinate from −20 to −20 + 100 = 80. His final position is (60, 80).Step 5: To find the distance from the starting point (0, 0) to (60, 80), use the Pythagorean theorem:Distance = sqrt(60^2 + 80^2) = sqrt(3600 + 6400) = sqrt(10000) = 100 m.

Verification / Alternative check:
Notice that (60, 80) is a scaled version of the classic 3–4–5 right triangle, with sides in the ratio 3:4:5 multiplied by 20. Here 60 = 3 * 20, 80 = 4 * 20, and the hypotenuse 100 = 5 * 20, confirming that the distance must be 100 m. This again matches our coordinate calculation and reinforces that no arithmetic mistake was made.

Why Other Options Are Wrong:
Distances such as 80 m or 140 m might appear if someone incorrectly added distances in a straight line or misapplied the Pythagorean theorem. A value like 260 m would correspond to summing all path segments, but the question asks for the straight-line distance from the starting point to the meeting point, not the total distance walked. Only 100 m is consistent with the correct geometry.

Common Pitfalls:
Students sometimes forget that repeated right turns change the facing direction, or they accidentally treat North as positive x instead of positive y when setting up coordinates. Others add all path distances rather than computing the resultant displacement. Drawing a quick sketch and labelling the coordinates at each key point is an excellent way to avoid these errors.

Final Answer:
The child meets his father at a point that is 100 m away from his starting point.