Walking at the speed of 6 km/hr, person reaches his office 8 minutes late. If he walks at the speed of 8 km/hr he reaches his office 3 minutes early. What is the distance between house and office ?

Let the usual time be t hours. Distance = 6(t + 8/60) = 8(t - 3/60). Solving: 6t + 48/60 = 8t - 24/60. This gives 2t = 72/60, so t = 36/60 = 0.6 hours. Distance = 6(0.6 + 8/60) = 6(0.6 + 0.133) = 6(0.733) = 4.4 km. Alternatively: time difference = 11 minutes at 6 km/hr, distance = 11/60 × 6 = 1.1 km extra. At 8 km/hr, this 1.1 km takes 1.1/8 hr = 8.25 minutes, but actual difference is 5 minutes, so we need to balance. Using the standard formula gives 4.4 km.