A man can row 12 km/hr in still water. When the river is running at 2.2 km/hr, it takes him 1.2 hours to row to a place and come back. How far is the place?

Correct option is B

Given:

Speed of the man in still water = 12 km/hr

Speed of the river = 2.2 km/hr

Total time for the round trip = 1.2 hours

Concept Used:

Speed downstream = Speed in still water + Speed of the river

Speed upstream = Speed in still water - Speed of the river

Time $$=\frac{\text{ Distance }}{\text{ Speed}}$$​​

Solution:
Let the distance to the place be x km.

Downstream speed = 12 + 2.2 = 14.2 km/hr

Upstream speed = 12 - 2.2 = 9.8 km/hr

Time taken to row downstream =$$\frac{x}{14.2}$$​hours

Time taken to row upstream $$= \frac{x}{9.8}$$​ hours

Total time = Time downstream + Time upstream
$$\frac{x}{14.2} + \frac{x}{9.8}$$​= 1.2 hours

$$\frac{x}{14.2} + \frac{x}{9.8} = 1.2 \\ \ \\\frac{x(9.8 + 14.2)}{14.2 \times 9.8} = 1.2 \\ \ \\\frac{x \times 24}{139.16} = 1.2 \\ \ \\x = \frac{1.2 \times 139.16}{24} \\ \ \\x = \frac{166.992}{24} = 6.958 \, \text{km}$$​