Correct Answer - Option 4 : 35 km
Given:
Speed of man in still water = 9 km/h
Speed of stream = 6 km/h
Total time taken = 14 hours
Concept used:
If the speed of a boat/man in still water be x km/h and the speed of the stream be y km/h, then
Speed of boat downstream = (x + y) km/h
Speed of boat upstream = (x - y) km/h
Speed = Distance/Time
Calculation:
Let the distance traveled by man be D km and time taken be t1 in downstream and t2 in upstream
Speed of man in downstream = (x + y) km/h
⇒ (9 + 6) = 15 km/h
Time, t1 = D/15 ----(1)
Speed of man in upstream = (x - y) km/h
⇒ (9 - 6) = 3 km/h
Time, t2 = D/3 ----(2)
Adding equations (1) and (2), we get
⇒ t1 + t2 = (D/15) + (D/3)
⇒ 14 = (5D + D)/15
⇒ 14 × 15 = 6D
⇒ (14 × 15)/6 = D
⇒ 7 × 5 = D
⇒ 35 km = D
∴ The place is 35 km far away.