Question : A boat takes 4 hours to travel from a place X to Y downstream and back from Y to X upstream. If the distance from X to Y is 10.5 km, and the speed of the current is 9 km/hr, then the speed of the boat in still water, in km/hr, is:
Option 1: $10 \frac{1}{2}$
Option 2: $15$
Option 3: $12$
Option 4: $12 \frac{1}{2}$
Correct Answer: $12$
Solution : Let the speed of the boat be $s$ km/hr. Speed of current = 9 km/hr Distance between X and Y = 10.5 km Upstream speed = $(s-9)$ km/hr Downstream speed = $(s+9)$ km/hr According to the question, $\frac{10.5}{(s-9)} + \frac{10.5}{(s+9)} = 4$ ⇒ $\frac{10.5(s+9 + s-9)}{(s^2-9^2)} = 4$ ⇒ $\frac{10.5×(2s)}{s^2-81} = 4$ ⇒ $10.5×(2s) = 4(s^2-81)$ ⇒ $21s = 4s^2-324$ ⇒ $4s^2-21s-324=0$ ⇒ $4s^2-48s+27s-324=0$ ⇒ $4s(s-12)+27(s-12)=0$ ⇒ $(4s+27)(s-12)=0$ ⇒ $s = 12$ [since speed can't be negative] Hence, the correct answer is $12$.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : A boat covers a distance of 72 km downstream in 6 hours, while it takes 12 hours to cover the same distance upstream. What is the speed of the boat in still water?
Question : A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in $6\frac{1}{2}$ hours. The speed of the current is:
Question : A boat can travel 104 km downstream in 8 hours. If the speed of the stream is 2 km/hr, then at what time will it be able to cover 13 km upstream?
Question : A boat can go 40 km downstream and 25 km upstream in 7 hours 30 minutes. It can go 48 km downstream and 36 km upstream in 10 hours. What is the speed (in km/hr) of the boat in still water?
Question : A boat travels 60 kilometres downstream and 20 kilometres upstream in 4 hours. The same boat travels 40 kilometres downstream and 40 kilometres upstream in 6 hours. What is the speed (in km/hr) of the stream?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile