972
Step 1: Define variables Let the distance between town A and town B = D km Speed of Arvind = 54 km/h Let the speed of Surbhi = v km/h After meeting: Arvind takes 6 hours to reach B → remaining distance = 54 × 6 = 324 km Surbhi takes 24 hours to reach A → remaining distance = 24 × v km Step 2: Use the ratio property The remaining distances after meeting are inversely proportional to their speeds: Arvind remaining distance / Surbhi remaining distance = Surbhi speed / Arvind speed Substitute values: 324 / (24 × v) = v / 54 Step 3: Solve for v 324 × 54 = 24 × v × v 17496 = 24 v^2 v^2 = 17496 / 24 = 729 v = 27 km/h Step 4: Find the total distance D Let t = time until they meet (in hours) Distance traveled by Arvind until meeting = 54 × t Distance traveled by Surbhi until meeting = 27 × t After meeting: Arvind remaining distance = 324 km Surbhi remaining distance = 27 × 24 = 648 km Total distance D can be written using both: D = Distance Arvind traveled + remaining distance = 54 × t + 324 D = Distance Surbhi traveled + remaining distance = 27 × t + 648 Equate both expressions: 54 × t + 324 = 27 × t + 648 54t - 27t = 648 - 324 27t = 324 t = 12 hours Step 5: Calculate total distance D D = 54 × 12 + 324 = 648 + 324 = 972 km Answer: 972 km