SSC CGL 2024 PYQ — Question 75

​​The correct answer is option 2 i.e.  $9\over4$.

The boatman rows to a place 30 km distant and back in 14 hours.

Let the boatman row 10 km downstream in x hours and 4 km upstream in x hours.

The downstream speed = 10/x

The upstream speed = 4/x

Then, $\frac{30}{10/x}+\frac{30}{4/x}=14$

⇒ 3x + 7.5x = 14

⇒ 10.5x = 14

⇒ x = 14/10.5 = 4/3

Downstream speed = 10/(4/3) = 15/2 km/h

Upstream speed = 4/(4/3) = 3 km/h

The speed of the stream = (Downstream speed - Upstream speed)/2

$=\frac{(15/2)-3}{2}=\frac{9/2}{2}=9/4$ km/h

Therefore, the speed (in km/h) of the stream is 9/4 km/h