GATE 2017 EC (EC2) – Question 4

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

Fatima starts at P, travels north 3 km and east 4 km to Q. She turns to face P and travels 15 km in that direction, then travels north 6 km. How far is she from P, and in which direction should she travel to reach P?

8 km, East
12 km, North
6 km, East
10 km, North

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Show answer and explanation

Correct answer: (A) 8 km, East

Explanation

Set P=(0,0), with east and north as positive coordinates. Then Q=(4,3), and the distance QP is 5 km.

The unit direction from Q toward P is $(−4/5,−3/5)$. Traveling 15 km gives displacement (−12,−9), so she reaches (−8,−6), continuing past P along the same line.

Moving north 6 km then takes her to (−8,0). She is **8 km west of P** and must travel **8 km east**, option **A**.

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