Mohan reaches the office 1 hour late when walking at 20 km/h. When he increases his speed to 25 km/h, he arrives 30 minutes early. What is the distance from home to office?

Introduction / Context:Schedule-variance problems compare actual travel time against scheduled time at two different speeds to deduce distance. The difference-of-reciprocals technique is standard.

Given Data / Assumptions:

• At 20 km/h: arrival is 1 hour late.
• At 25 km/h: arrival is 30 minutes early.
• Same route and scheduled arrival time.

Concept / Approach:Let distance be d and scheduled time be T_s (hours). Then d/20 = T_s + 1 and d/25 = T_s − 0.5. Subtract the equations to eliminate T_s and solve for d.

Step-by-Step Solution:d/20 − d/25 = 1.5d * (1/20 − 1/25) = 1.5d * (5 − 4)/100 = 1.5 → d/100 = 1.5d = 150 km.

Verification / Alternative check:T_s from the second equation: T_s = d/25 + 0.5 = 150/25 + 0.5 = 6 + 0.5 = 6.5 h. First equation check: 150/20 = 7.5 h = 6.5 + 1, consistent.

Why Other Options Are Wrong:100 km and 125 km do not satisfy both timing relations simultaneously.

Common Pitfalls:Mixing up the early/late signs; using minutes without converting to hours consistently.

Final Answer:150 km