SSC CGL 2022 PYQ — Question 61

The correct answer is option 4 i.e. 7,

Given:

Anup can row 33 km downstream and 35 km upstream in 8 hours

He can also row 44 km downstream and 28 km upstream in 8 hours

Concept Used:

Time = Distance/speed

Downstream speed = speed of boat + speed of stream

Upstream speed = speed of boat - speed of stream

Calculations:

Let the speed of boat and stream be x and yy respectively;

So, 

Downstream speed = x + y

Upstream speed = x - y

According to the question, we get:

⇒ $\dfrac{33}{x + y} +\dfrac{35}{x + y} = 8$       ----- (1)

⇒ $\dfrac{44}{x + y} + \dfrac{28}{x - y} = 8$        ----- (2)

Subtracting equation (1) from (2):

⇒ 11 × (x - y) = 7 × (x + y)

⇒ 11x - 11y = 7x + 7y

⇒ 4x = 18y

⇒ x = 9/2y

Using the value of x in equation (1), we get:

y = 2 and x = 9

Time required to travel 55 km downstream and 14 km upstream = $\dfrac{55}{x + y} + \dfrac{14}{x - y}$

⇒ 55/11 + 14/7

⇒ 5 + 2 = 7 hours

Hence the time taken to row 55 km downstream and 14 km upstream is 7 hours.