Question

A boat whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
A)10
B)5
C)6
D)5

Answer 1

Ans is option (d) 5 Km/hr

Answer 2

Speed of the water body is 5 km/hr.

Solution:  

Let x km/hr be speed of water body.

15 km/h is speed of boat in standing water. Therefore, total speed with which boat moves with current is (15+x) km/h.

Therefore time taken by boat to move with the current is $\frac{30}{15+x}$hr

Similarly, boat travelling time to move against the current of a distance of 30 km is $\frac{30}{15-x}$ h r

The total time travelled by boat to move with current and against the current is  

$\begin{array}{l}{\frac{30}{15-x}+\frac{30}{15+x}=4.5} \\ \\{450-30 x+450-30 x=4.5\left(225-x^{2}\right)} \\ \\{\frac{900}{4.5}=\left(225-x^{2}\right)} \end{array}$

Evaluating for x, we get x = 5 km/h which means that speed of water body is 5 km/h.