Correct Answer - Option 1 : 8 : 3
Given:
Boat takes time to cover a certain distance upstream = 8 hours 48 minutes
Boat takes time to cover the same distance downstream = 4 hours
Formula Used:
Speed = Distance/Time
Calculation:
Let speed of boat in still water be x km/h
Let speed of current be y km/h
Let the certain distance be D km
Upstream speed = (x – y) km/h
Downstream speed = (x + y) km/h
8 hours 48 minutes = 44/5 hours
D/(x + y) = 4 .....(i)
D/(x – y) = 44/5 .....(ii)
Dividing equation (i) by (ii)
\(⇒ \frac{{\frac{D}{{\left( {x + y} \right)}}}}{{\frac{D}{{\left( {x\;-{\rm {y}}} \right)}}}} = \;\frac{4}{{\frac{{44}}{5}}}\)
⇒ (x – y)/(x + y) = (4 × 5)/44
⇒ 44 (x – y) = 20 (x + y)
⇒ 44x – 44y = 20x + 20y
⇒ 44x – 20x = 20y + 44y
⇒ 24x = 64y
⇒ x/y = 64/24
⇒ x/y = 8/3
⇒ x : y = 8 : 3
∴ The ratio between the speed of the boat and speed of the water current is 8 : 3
