Xavier Aptitude Test 2023 Paper

Question : 56 of 102

Marks: +1, -0

The problem below consists of a question and two statements numbered

1 & 2

.
You have to decide whether the data provided in the statements are sufficient to answer the question.
Rahim is riding upstream on a boat, from point

A

B

, at a constant speed. The distance from

A

B

is 30 km . One minute after Rahim leaves from point

A

, a speedboat starts from point

A

to go to point

B

. It crosses Rahim's boat after 4 minutes. If the speed of the speedboat is constant from

A

B

, what is Rahim's speed in still water?
1. The speed of the speedboat in still water is

30 {\km} \/ {\hour}

.
2. Rahim takes three hours to reach point

B

from point

A

Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient
Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient
Each statement alone is sufficient
Both statements together are sufficient, but neither of them alone is sufficient
Statements $1 & 2$ together are not sufficient

Validate

Solution:

Let '

a

' and '

b

' be the speeds of Rahim and the speed boat in still water, respectively
Let 'c' be the speed of the stream.
Speed boat starts after 1 minute of Rahim's departure and crosses him after 4 minutes.
It implies that the speed boat covered the same distance in 4 minutes that Rahim took 5 minutes.
Hence, the ratio of upstream speeds of Rahim and Speed boat

=\;{a-c}/{b-c}=\;{4}/{5}

Using Statement 1, we get

b=30 {\kmph}

. But, it's not sufficient to get the value of 'a'.
Using Statement 2 , we get

a-c=\;{30}/{3}=10 {\kmph}

. But it's also not sufficient to get the value of 'a'. using both statements, we get

\;\;{a-c}/{b-c}=\;{4}/{5}

\;\;{10}/{30-c}=\;{4}/{5}

\;50=120-4 c

\;c=17.5

\;a=17.5+10=27.5 {\kmph}

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