SSC CPO 2024 PYQ — Question 139

The correct answer is option 4 i.e. $7\over24$.

Given that, time taken by man to travel 48 km and back = 48 hours

Let the time taken by the man to row upstream and downstream be x hours.

Distance = speed × time

According to the given question,

Speed for travelling 4 km with the stream = 4/x km/h

Speed of travelling 3 km against the stream = 3/x km/h

Now, ${48 \over {4 \over x}} + {48 \over {3 \over x}}$ = 48

⇒ ${x \over 4} + {x \over 3}$ = 1

⇒ 7x = 12

⇒ x = $12 \over 7$

So, downstream speed, (a + b) = ${4 \over {12 \over 7}}$ = $7 \over 3$ km/h   ...(i)

Upstream speed, (a - b) =  ${3 \over {12 \over 7}}$ = $7 \over 4$ km/h   ...(ii)

Where a is the speed of boat in still water and b is the speed of stream.

Subtracting equation (ii) from equation (i),

⇒ 2b = ${7 \over 3} - {7 \over 4}$

⇒ 2b = $7 \over 12$

⇒ b = $7 \over 24$

Hence the speed of the stream (in km/h) is $7 \over 24$.