NIMCET 2023
Two friends A and B were standing at diagonally opposite corners of a rectangular plot whose perimeter is 100 m. A first walked x metres along the length of the plot towards the East and then y metres towards the South. B walked x metres along the breadth towards the North and then y metres towards the West. At the end of their walks, A and B were standing at diagonally opposite corners of a smaller rectangular plot whose perimeter is 40 m. How much distance did A walk?
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Answer: Option C — 15 m
Detailed Solution
Let the length (east-west) be L and the breadth W, so . A starts at the north-west corner and B at the south-east corner .
A ends at and B at . The new plot has sides and .
, so . A walked m.
✓ Check
Take , , , : A ends at and B at , giving sides 15 and 5 and perimeter 40.⚠ Common trap
(B) 25 m halves the semi-perimeter 50; but each side shrinks by , so .Quick tip
Each side of the new plot is shorter by :
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Ask a doubtMore Direction Sense Questions
View all ›- Q1.A man is facing north-west. He turns 90° in the clockwise direction and then 135° in the anticlockwise direction. Which direction is he facing now?
- Q2.Sachin walks 20 m towards the South from point P. He then turns left and walks 30 m, turns left again and walks 20 m, and then turns left once more and walks 40 m to reach point Q. How far and in which direction is point Q from point P?
- Q3.Vikram starts from a point and walks 18 metres towards the West. He then turns left and walks 14 metres. After that, he turns right and walks 11 metres. He again turns right and walks 7 metres. Then he turns left and walks 16 metres. Finally, he turns right and walks 9 metres. In which direction is he facing at the end?
- Q4.A man travels to the north and turns east and travels , and again he turns north and travels and again turns to the east and travels . How far is he from the starting point?
- Q5.A man travels to the north and turns east and travels , and again he turns north and travels and again turns to the east and travels . How far is he from the starting point?
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Direction Sense — Preparation
This question tests your understanding of Direction Sense, a key topic in the Logical Reasoning section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Direction sense questions describe a person's movements, such as walking 5 km north and then turning right, and ask for the final direction or distance from the starting point. This topic covers the four main and four intermediate directions, left and right turns, shadow-based questions using the position of the sun, and coded direction questions. Always draw a rough diagram as you read each step. For the shortest distance between the start and end points, use the Pythagorean theorem on the net north-south and east-west distances. Remember that the sun rises in the east, so in the morning a person's shadow falls to the west, and in the evening it falls to the east. A right turn from north points east, and a left turn from north points west. Practise the direction sense questions below, each with a step-by-step diagram solution.