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Solutions
Given:-
Luxury Bus B - start from City S to reach City A
Luxury Bus Z - start from City U to reach City A
Now,
Journey of Bus B:
1) Bus B starts moving 12 km in the south direction to reach town R then takes a right turn and moves 18 km to reach town P, then takes a left turn and moves 6 km to reach city A. Bus B starts moving from city S 12 km in the south direction.
2) Towns P, Q, and R lie in the same line, and the distance between P and Q is half of the distance between towns Q and R.
It means PR = PQ + QR and PQ = QR/2. Also PR = 18 km. So,
18 = QR/2 + QR
18 = (QR + 2QR)/2
36 = 3QR
QR = 36/3 = 12 km.
PQ = QR/2 = 12/2 = 6 km.

Journey of Bus Z:
1) Bus Z starts to move 18 km toward the south and reaches town W, then takes a left turn and moves 2 km more than the distance between towns Q and R to reach city A. Bus Z starts moving from city U 18 km in the south direction. Distance between Q ad R = 12 km. 2 km more means 12 + 2 = km is the distance between town W and city A.
2) Town V lies between U and W. It means UW = UV + VW
3) The distance between V and W is double the distance between U and V. It means VW = 2(UV)
So, UW = UV + 2(UV)
18 = 3(UV)
UV = 6 km
VW = 12 km

Combining the journey of bus B and Z, we get,

The shortest route from the following from town V to city A -
1) Back to town W then go to city A from there → VW + WA = 12 + 14 = 26 km
2) From town V he should go 14 km in the east direction and then move south to reach city A → 14 + 6 + 6 = 26 km
3) From town V he should go north to reach point U from there, he should reach town S, then town R, then P, and then city A. → 6 + 32 + 12 + 18 + 6 = 74 km.
Both 1) and 2) are equal and shortest routes.
Hence, the correct answer is BBack to town W then go to city A from there.