A man travelled a certain distance by a car and covered half of his journey. Out of the remaining distance, five-sixths was done travelling in a van and the rest by auto. If the distance covered
by auto was 5 km, what was the distance he travelled totally?
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A.
60 km
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B.
45 km
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C.
72 km
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D.
48 km
Correct Answer:
A. 60 km
Explanation:
To find the total distance, let the entire journey be represented by x. According to the problem, the man first covers half of this distance by car, which is x/2. This leaves a remaining distance of x - x/2, which equals x/2. Next, he travels five-sixths of this remaining portion by van. Therefore, the distance covered by van is (5/6) * (x/2) = 5x/12. To find the final portion covered by auto, we subtract the van distance from the remaining distance: (x/2) - (5x/12). By using a common denominator of 12, this becomes (6x/12) - (5x/12) = x/12. The problem states that this final auto distance is 5 km. By setting up the equation x/12 = 5 and multiplying both sides by 12, we find that x = 60. Thus, the total distance traveled was 60 km.
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