# A boat running upstream takes 8 hours 48 minutes to cover a certain distance while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively? (A) 2:1 (B) 3:2 (C) 8:3 (D) 3:8

Given, distance covered by man, upstream in 8 hrs 48 min is equal to the distance covered by him downstream in 4 hrs.

Let,

Man’s upstream rate = x kmph

Downstream rate = y kmph

Now as per the given question,

x × 8 4/5 = y × 4

44/5 x = 4y

y = 11/5 x

or

x/y = 5/11 ………..(i)

Speed of boat = (x+y)/2

Speed of water stream = (y-x)/2

Therefore, the required ratio is:

[(x+y)/2]/[(y-x)/2]

(x+y)/(y-x)

(x/y+1)/(1-x/y)

Now putting the value of x/y from eq.(i), we get;

$$=\frac{\frac{5}{11}+1}{1-\frac{5}{11}}\\ =\frac{\frac{5+11}{11}}{\frac{11-5}{11}} \\ = \frac{16}{6} \\ = \frac{8}{3}$$