Paper 1 · Mathematical Reasoning and Aptitude
UGC NET December 2023 (19.12.2023) Shift-II
A child is looking for his father. He goes 10 metres towards east and then turns to his right and goes 30 metres. From there the child again turns to his right and goes for 40 metres, where he finds his father at his uncle's place. How far is his uncle's place from the starting point of the child?
A30√5 metre ✓ Correct
B40 metre
C40√5 metre
D30√2 metre
Correct answer: (A) 30√5 metre — The uncle's place is 30 root 5 metres from the start, so the answer is 30 root 5 metre.
Explanation
★The uncle's place is 30 root 5 metres from the start, so the answer is 30 root 5 metre.
★The child's path turns twice at right angles, forming an L shaped route.
★The straight line distance from start to end is the hypotenuse of a right triangle.
★The two perpendicular displacements work out to 60 metres and 30 metres.
★By the Pythagoras theorem, distance is the square root of 60 squared plus 30 squared.
★That is the square root of 4500, which equals 30 root 5 metres.
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