Question

If time upstream = n × time downstream and speed in still water is 'x' and speed of stream is 'y', then find x : y.

• A. $$\frac{n}{2}$$
• B. $$\frac{(n-1)}{(n+1)}$$
• C. $$\frac{n}{(n-1)}$$
• D. $$\frac{(n+1)}{(n-1)}$$

Answer 1

Answer:

$$\frac{(n+1)}{(n-1)}$$

Speed of boat in still water = x

Speed of current = y

Upstream speed = x - y

Downstream speed = x + y

If time upstream = n $\times$ time downstream

Time ratio of upstream to downstream = n : 1

As we know,

Speed is inversely proportional to time, then

Speed ratio of upstream to downstream = 1 : n

(x - y) : (x + y) = 1 : n

$⇒\frac{(x-y)}{(x+y)}=\frac{1}{n}$

$⇒\frac{(x+y)}{(x-y)}=\frac{n}{1}$

Componendo or Dividendo

$\frac{x}{y}=\frac{(n+1)}{(n-1)}$

⇒ x : y = (n + 1) : (n - 1)