JIPMAT 2021 (QA) - A man rows 20 km upstream and back again to the starting point in 110 minutes. If the speed of the stream is 2 kmph, then the speed of rowing in still water is | PYQs + Solutions

JIPMAT 2021

Arithmetic

Time, Speed & Distance

Conceptual

A man rows 20 km upstream and back again to the starting point in 110 minutes. If the speed of the stream is 2 kmph, then the speed of rowing in still water is

20 kmph

22 kmph

24 kmph

28 kmph

Correct Option: 2

Let speed of rowing in still water =

x

kmph

Upstream speed =

x - 2

kmph (rowing speed

-

stream speed)

\newline

Downstream speed =

x + 2

kmph (rowing speed

+

stream speed)

Time equation:

\frac{20}{x-2} + \frac{20}{x+2} = \frac{110}{60}

(because we have to convert minutes to hours)

\frac{20(x+2)+20(x-2)}{(x-2)(x+2)}=\frac{110}{60}

\frac{20x+40+20x-40}{(x-2)(x+2)}=\frac{110}{60}

40x(60)=110(x-2)(x+2)

2400x=110(x^2-4)

[(a+b)(a-b)=a^2-b^2]

2400x=110x^2-440

110x^2 - 2400x - 440 = 0

Solve quadratic:

\newline

x = 22

x = -0.2

(reject negative)

Therefore, speed of rowing in still water is 22 kmph.