Question:
Ravi is standing at Lal Chowk facing towards East. He turns 90° towards his right and walks 'x' km to reach Shiv Mandir. Then he turns 90° towards his left and walks 3 km to reach Ganesh Chowk. The shortest distance between Lal Chowk and Ganesh Chowk is 5 km. What is the distance between Lal Chowk and Shiv Mandir?
Ravi is standing at Lal Chowk facing towards East. He turns 90° towards his right and walks 'x' km to reach Shiv Mandir. Then he turns 90° towards his left and walks 3 km to reach Ganesh Chowk. The shortest distance between Lal Chowk and Ganesh Chowk is 5 km. What is the distance between Lal Chowk and Shiv Mandir?
Updated On: Sep 16, 2026
- 3 km
- 4 km
- 5 km
- 25 km
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Step 1: Trace Ravi's first move.
Ravi starts at Lal Chowk facing East.
He turns 90° to his right, so he now faces South, and walks x km south to reach Shiv Mandir.
Step 2: Trace Ravi's second move.
At Shiv Mandir (facing South) he turns 90° to his left, so he now faces East.
He walks 3 km east to reach Ganesh Chowk.
Step 3: Set up the right triangle.
The two legs of the path (x km south, then 3 km east) meet at a right angle at Shiv Mandir.
The straight-line distance from Lal Chowk to Ganesh Chowk, given as 5 km, is the hypotenuse of this right triangle.
Step 4: Apply the Pythagoras theorem.
x² + 3² = 5²
x² = 25 - 9 = 16
x = 4 km.
Final Answer: 4 km (option 2)
- In direction-sense problems, sketch the actual path as a sequence of right-angle turns.
- When the final "straight-line distance" is asked and the path forms a right angle, apply the Pythagoras theorem: (hypotenuse)^2 = (leg 1)^2 + (leg 2)^2.
Step 1: Trace Ravi's first move.
Ravi starts at Lal Chowk facing East.
He turns 90° to his right, so he now faces South, and walks x km south to reach Shiv Mandir.
Step 2: Trace Ravi's second move.
At Shiv Mandir (facing South) he turns 90° to his left, so he now faces East.
He walks 3 km east to reach Ganesh Chowk.
Step 3: Set up the right triangle.
The two legs of the path (x km south, then 3 km east) meet at a right angle at Shiv Mandir.
The straight-line distance from Lal Chowk to Ganesh Chowk, given as 5 km, is the hypotenuse of this right triangle.
Step 4: Apply the Pythagoras theorem.
x² + 3² = 5²
x² = 25 - 9 = 16
x = 4 km.
Final Answer: 4 km (option 2)
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