A boat takes 1 hour 30 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 km/hr, then the speed of the stream is:

2 km/hr

The correct answer is Option (1) → 2 km/hr

Let the speed of the stream be x km/hr.

Speed downstream = 10 + x km/hr, speed upstream = 10 - x km/hr

Distance = 36 km

Time difference: 1 hour 30 minutes = 3/2 hours

Time = Distance / Speed

Time upstream - Time downstream = 3/2

$\frac{36}{10 - x} - \frac{36}{10 + x} = \frac{3}{2}$

Take LCM:

$36 \cdot \frac{(10 + x) - (10 - x)}{(10 - x)(10 + x)} = \frac{3}{2}$

$36 \cdot \frac{2x}{100 - x^2} = \frac{3}{2}$

$\frac{72x}{100 - x^2} = \frac{3}{2}$

Cross multiply:

$x^2 + 48x - 100 = 0$

Solve quadratic:

x = $\frac{-48 \pm \sqrt{48^2 + 400}}{2} = \frac{-48 \pm \sqrt{2304 + 400}}{2} = \frac{-48 \pm \sqrt{2704}}{2}$

x = $\frac{-48 \pm 52}{2}$

Take positive root:

x = $\frac{-48 + 52}{2} = \frac{4}{2} = 2$ km/hr