A man can row 71/2 km/h in still water. If in a river

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A man can row 7¹/₂ km/h in still water. If in a river running at 1.5 km/h, it takes him 50 min to row to a place and back, how far off is the place ?

1. 3 km
2. 4 km
3. 1 km
4. 2 km

Correct Option: A

Let the distance be L km.
Speed of the main in still water = 7¹/₂ km/h
and speed of the river = 15 km/h

∴ Speed of the man downstream = 7.5 + 1.5 = 9
Speed of the man upstream = 7.5 - 1.5 = 6 km/h

According to the question,
L/9 + L/6 = 50/60
⇒ (4L + 6L)/36 = 50/60
⇒ 10L/36 = 50/60
⇒ L = (50 x 36)/(10 x 60)
5⇒ x = 3 km