JIPMAT 2022 (QA) - Given below are two statements based on the following: motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Statement I: Speed of the boat in still water is 12 km per hour. II: Speed of the stream is 4 km per hour. the light of the above statements, choose the correct answer from the options given below: | PYQs + Solutions

JIPMAT 2022

Arithmetic

Time, Speed & Distance

Medium

Given below are two statements based on the following:
A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours.
Statement I: Speed of the boat in still water is 12 km per hour.
Statement II: Speed of the stream is 4 km per hour.
In the light of the above statements, choose the correct answer from the options given below:

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is false but Statement II is true

Statement I is true but Statement II is false

Correct Option: 3

Let speed in still water =

x

km/hr

\newline

Stream speed =

y

km/hr

From first journey (30 km upstream + 28 km downstream in 7 hours):

\newline

\frac{30}{x-y} + \frac{28}{x+y} = 7

...(1)

From second journey (21 km upstream + 21 km downstream in 5 hours):

\newline

\frac{21}{x-y} + \frac{21}{x+y} = 5

...(2)

For Statement II (

y = 4

\newline

From equation (2):

\newline

\frac{21}{x-4} + \frac{21}{x+4} = 5

\frac{42x}{(x-4)(x+4)} = 5

42x = 5(x^2-16)

5x^2 - 42x - 80 = 0

Solving quadratic:

\newline

a = 5

b = -42

c = -80

x = \frac{-b ± \sqrt{b^2-4ac}}{2a}

x = \frac{42 ± \sqrt{1764+1600}}{10}

x = \frac{42 ± \sqrt{3364}}{10}

x = \frac{42 ± 58}{10}

x = 10

(ignore the negative alternative)

Verifying

x = 10

and

y = 4

in equation (1):

\newline

\frac{30}{6} + \frac{28}{14} = 5 + 2 = 7

✓

Therefore Statement II (

y = 4

) is true and

x = 10

(not 12)

\newline

So Statement I (

x = 12

) is false.