Discussion
Ram and Rohan leave their respective houses to meet each other. Ram walks a distance of 3 km towards the north, then turns to his left and walks 2 km. He again turns left and walks 3 km. At this point, he turns to his left and walks 5 km. Meanwhile, Rohan walks a distance of 5 km towards the south, then turns to his left and walks 1 km. He again turns left and walks 5 km. He then turns to his left and walks for 5 km and meets Ram. What is the shortest distance between their houses?
Answer: C
Place Ram's house at the origin. Ram goes 3 km north, 2 km west, 3 km south and 5 km east, ending 3 km east of his house. Rohan goes 5 km south, 1 km east, 5 km north and 5 km west, so he ends 4 km west of his own start.
\[ x_R - 4 = 3 \Rightarrow x_R = 7 \]
Rohan's house is on the same line as Ram's, at 7 km to the east. So the shortest distance between the houses is 7 km. The options 9, 6 and 5 km do not agree with this meeting point.
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