Question

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 downsteam. What is the ratio between the speed of the boat and the speed of the water current respectively?

(a) 2 : 1

(b) 3 : 1

(c) 8 : 3

(d) Cannot be determined

Answer 1

Correct option is (c) 8 : 3

Let the man's rate upstream be x kmph and that downstream be y kmph.

Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

⇒ \((x \times 8\frac 45) = (y \times 4)\)

⇒ \(\frac{44}4x = 4y\)

⇒ \(y = \frac{11}5 x\)

Required ratio = \(\left(\frac{y + x}2\right) :\left(\frac{y - x}2\right)\)

\(= \left(\frac{16x}5 \times \frac 12\right) : \left(\frac{6x}5 \times \frac 12\right)\)

\(= \frac 85 :\frac 35\)

\(= 8:3\)