CMAT Exam 2023 Shift 2 Solved Paper

Question : 8 of 100

Marks: +1, -0

Given below are two statements :
Statement I: Ravi walks from his house at a speed of

5 {\km}

per hour and reaches the college 10 minutes late. If he increases the speed by

1 {\km}

per hour next day, he reaches the college 4 minutes earlier than the scheduled time. If the college is

{\P} {\km}

far from his house, then

{\P}=7.5 {\km}

.
Statement II: Amit runs

2 \;{1}/{3}

times as fast as Babita. If Amit gives Babita a start of 80 meters, then the winning post must be 140 meters far so that Amit and Babita might reach it at the same time. 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 true but Statement II is false
Statement I is false but Statement II is true

Validate

Solution:

Statement I:
Let the actual time taken by Ravi to reach the college be '

t

'.
If Ravi travels at a speed of

5 {\km} \/ {\hr}

, time taken is

{\t}+\;{10}/{60}

If Ravi travels at a speed of

6 {\km} \/ {\hr}

, time taken is

{\t}-\;{4}/{60}

Distance

=

speed*time

= {\P}=5 (t+\;{10}/{60}) =6 (t-\;{4}/{60})

5 (t+\;{10}/{60}) =6 (t-\;{4}/{60})

5 t+\;{50}/{60}=6 t-\;{24}/{60}

t=\;{74}/{60}

Distance

(P)=5 (\;{74}/{60}+\;{10}/{60}) =5 (\;{84}/{60}) =7 {\km}

Therefore, statement I is incorrect.
Statement II:
Let the speed of Babita be

3 x

.
The speed of Amit is

7 {\x}

B covers distance

y

.
In the same time, A should cover

80+y

\;\;{y}/{3 x}=\;{80+y}/{7 x}

\;7 y=240+3 y

\;4 y=240

\;y=60

Total distance

=80+60=140 {\m}

Therefore, statement II is correct.
The answer is option D.

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