If the ratio of speed upstream and downstream is 5 : 7 and the speed of the stream is 6m/sec, then what is the time taken by a boat to cover the total distance of 210 m bothupstream and downstream?

Correct option is D

Given:

Ratio of upstream to downstream speed = 5 : 7

Speed of stream = 6 m/sec

Total distance = 210 m

Formula Used: 

Distance = Speed $$\times$$ Time​

Solution:

Let the speed of the boat in still water be x

Then,

Upstream speed = x - 6

Downstream speed = x + 6

And the ratio is given:

​$$\frac{x - 6}{x + 6} = \frac{5}{7}$$​​

Applying componendo and dividendo

​$$\frac{x}{6} = \frac{12}{2}$$​​

​$$\implies x = 36$$​​

So,

Upstream speed = 36 - 6 = 30 m/sec

Downstream speed = 36 + 6 = 42 m/sec 

To cover 210m upstream and downstream

Upstream time = $$\frac{210}{30}$$​ = 7 sec

Downstream time = $$\frac{210}{42}$$​ = 5 sec

Total time = 7 + 5 = 12 seconds