Sohail reaches his office 5 minutes late when walking at 16 km/h, and 10 minutes early when walking at 20 km/h. Find the one-way distance from his home to his office (in km).

Introduction / Context:When departure time is fixed, early/late arrival relative to schedule gives two equations for the same distance at different speeds. The total early–late gap is 15 minutes (0.25 h) between the two scenarios.

Given Data / Assumptions:

• D/16 = T + 5/60.
• D/20 = T − 10/60.
• D is the distance; T is the scheduled time (unknown).

Concept / Approach:Subtract the equations to eliminate T: D/16 − D/20 = 15/60 = 1/4 hour. Solve for D.

Step-by-Step Solution:

Verification / Alternative check:Check times: 20/16 = 1.25 h (5 min late if T = 1.1667 h); 20/20 = 1.0 h (10 min early)—consistent.

Why Other Options Are Wrong:16, 18, 22, 24 km do not satisfy the 15-minute difference produced by 16 vs 20 km/h.

Common Pitfalls:Adding instead of subtracting the equations; mixing minutes with hours.

Final Answer:20 km