Q.8 The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car had travelled when the cars crossed each other?
(A) 66.6
(B) 75.2
(C) 88.2
(D) 116.5

Car P starts from Delhi to Agra (233 km), while car Q starts from Agra to Delhi 1 hour later. They meet 75 minutes after Q starts, with P’s speed 10 km/hr faster than Q’s. This classic relative speed problem reveals exactly how far each traveled at the meeting point.

Problem Setup

Let Q’s speed be v km/hr, so P’s speed is v + 10 km/hr.

P travels alone for 1 hour (covering v + 10 km), then both travel for 75 minutes (1.25 hours) until they meet.

The remaining distance between them at Q’s start is:

233 − (v + 10) km

This distance is covered in 1.25 hours by their combined speeds:

(v + 10 + v) × 1.25 = 233 − (v + 10)

Simplifying:

• 3.25v + 12.5 = 233 − v − 10
• 4.25v = 230.5
• v = 54.235 km/hr

P’s speed = 64.235 km/hr

Distance Traveled by Car P

P travels total time 1 + 1.25 = 2.25 hours at 64.235 km/hr.

Correct Answer: (C) 88.2 km

Verification:

• Q travels: 1.25 × 54.235 ≈ 67.8 km
• P travels head start: 64.2 km
• Plus joint travel: ≈ 23.9 km
• Total P distance ≈ 88.2 km

Combined distances align perfectly to close the full 233 km.

Why Other Options Are Wrong

• (A) 66.6 km: Matches Q’s distance only, ignoring P’s extra 10 km/hr.
• (B) 75.2 km: Assumes identical speeds.
• (D) 116.5 km: Overestimates by assuming no head start or half distance.

Speed Breakdown Table