Directions: Select the correct alternative from the given choices. The distance between two cities, A and B, is partly uphill, partly on level ground and partly downhill. It took three hours for a bus to go from A to B, whereas it took 40 minutes more to make the return journey. Find the distance (in km) between A and B, if the uphill speed, the downhill speed and that on the level ground of the bus are 40 km/hr, 50 km/hr and 48 km/hr respectively?

Let the distance uphill, on level ground, and downhill from A to B be x, y, and z kilometers respectively. The time from A to B is given by the equation x/40 + y/48 + z/50 = 3, and the return journey time is z/40 + y/48 + x/50 = 3 + 40/60, which equals 11/3 hours. Adding the two equations and grouping the terms yields x times 9/200, plus y times 1/24, plus z times 9/200, equals 20/3; since y/24 equals 0, solving these simultaneous equations gives the total distance x + y + z = 160 km.

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