Q.21 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 21 Solution

Topic: Motion in a Straight Line · Official NTA Booklet Code 45

Question

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

✓

Verified Against NTA Final Answer Key

Option (4) : 15 min, 120 km/h

📚 Motion in a Straight Line Medium

📋 Given Parameters & Problem Setup

Bus Interval Leaves every T minutes in either direction

Girl’s Speed (v_g) 60 km/h from X to Y

Overtaking Interval (Same Direction) t₁ = 30 minutes

Crossing Interval (Opposite Direction) t₂ = 10 minutes

⚡

The 30-Second Exam Hall Shortcut: ⚡ Bus Schedule Sum-and-Difference Rule

⏱️ Save ~50 seconds

(v_b - 60) × 30 = (v_b + 60) × 10 ⟹ 3(v_b - 60) = v_b + 60 ⟹ 2v_b = 240 ⟹ v_b = 120 km/h! T = (120 - 60) × 30 / 120 = 15 min!

1 Spatial distance between consecutive buses in same direction: d = v_b · T.

2 In same direction: relative speed is (v_b - 60), time is 30 min ⟹ d = (v_b - 60) × 30.

3 In opposite direction: relative speed is (v_b + 60), time is 10 min ⟹ d = (v_b + 60) × 10.

4 Equate: 30(v_b - 60) = 10(v_b + 60) ⟹ 3v_b - 180 = v_b + 60 ⟹ 2v_b = 240 ⟹ v_b = 120 km/h.

5 Calculate T: d = 120 × T = (120 - 60) × 30 = 1800 ⟹ T = 1800 / 120 = 15 min.

6 Pick Option (4) in under 25 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Equations of Motion under Constant Acceleration (NCERT Physics · Motion in a Straight Line: v = u + at, s = ut + ½at²).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formulate Distance Between Consecutive Buses

Buses depart in either direction every T minutes at constant speed v_b. The spatial separation between any two successive buses traveling in the same direction is constant:

d = v_b \cdot T

• T is in minutes; v_b is in km/h.

Step 2

Equations of Relative Motion

For motion in the same direction, the relative speed is (v_b - 60) km/h and the time taken to cover distance d is 30 minutes. For motion in the opposite direction, relative speed is (v_b + 60) km/h and time is 10 minutes:

d = (v_b - 60) \times 30 = (v_b + 60) \times 10

• 3(v_b - 60) = v_b + 60 ⟹ 3v_b - 180 = v_b + 60 ⟹ 2v_b = 240 ⟹ v_b = 120 km/h.

Step 3

Calculate Bus Departure Interval T

Substitute v_b = 120 km/h back into either distance expression:

120 \cdot T = (120 - 60) \times 30 = 60 \times 30 = 1800 \implies T = \frac{1800}{120} = 15\text{ minutes}

• Bus speed = 120 km/h, Bus interval T = 15 min.
• Corresponds uniquely to Option (4).

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. A bus speed of 40 km/h is less than the girl’s speed (60 km/h), so buses going in her direction could never overtake her.

⚠️

Student Fallacy (Why candidates pick this trap): Ignoring the physical constraint that v_b must exceed v_girl to overtake.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Does not satisfy relative distance equations.

⚠️

Student Fallacy (Why candidates pick this trap): Arbitrary guess.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. For v_b = 90 km/h, same-direction relative speed is 30 km/h; ratio would not yield 30 min.

⚠️

Student Fallacy (Why candidates pick this trap): Algebraic slip in 2v_b = 240.

4 D

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. v_b = 120 km/h and T = 15 min satisfy both relative motion equations.

💡

Why this is airtight: None; classic NCERT problem.

⚠️

NTA Trap Alert: v_bus Less Than v_girl Impossibility

Option (1) gives v_b = 40 km/h. If the bus travels at 40 km/h and the girl travels at 60 km/h, a bus behind her could NEVER overtake her! Eliminating options with v_b ≤ 60 immediately rules out Option 1.

🛡️ How to avoid the -1 mark: Sanity check: Overtaking requires v_bus > v_girl.

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Core NEET Syllabus Standard

NEET Physics Core Syllabus · Motion in a Straight Line Standard Benchmark

Core Scientific Principle Tested:

"Relative velocity v_rel = v₁ - v₂ for same direction and v₁ + v₂ for opposite direction."

Syllabus Focus: Relative Velocity in One Dimension

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

30(v - 60) = 10(v + 60) ⟹ 2v = 240 ⟹ v = 120 km/h and T = 15 min!

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NEET 2025 Physics Question 21 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Bus Schedule Sum-and-Difference Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Formulate Distance Between Consecutive Buses

Equations of Relative Motion

Calculate Bus Departure Interval T

360° Option Elimination Engine Key Feature

NTA Trap Alert: v_bus Less Than v_girl Impossibility

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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