CAT Exam Model Paper 4 with solutions for free online practice

Question : 59 of 60

Marks: +1, -0

The question given below is followed by two statements, A and B. Mark the answer using the following instructions:
Mark (a) if the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.
Mark (b) if the question can be answered by using either statement alone.
Mark (c) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
mark (d) if the question cannot be answered even by using both the statements together
Q. A train started from point P towards point Q and met with an accident after traveling 30 km. The train’s speed got reduced because of the accident and it finally reached Q 16 minutes late. What is the distance covered by the train between P and Q?
A. The train would have reached 21 minutes late had the accident taken place 20 km after P.
B. The train would have reached 12 minutes late had the accident taken place 20 km before Q.a

Validate

Solution:

Let us assume that the accident happens at point A.
Hence PA and AQ would be the distances covered by the train from P to A and A to Q respectively.

Let the speed (in km/min) before and after the accident be V and ‘u'.
Total time taken by the train had the accident not taken place

= { P Q } /{ v } = { ( P A + A Q ) } /{ v }

Total time taken by the train due to accident

= { P A }/ { v } + { A Q } /{ U } = { P Q } /{ v } + 16 = { P A }/ { v } + { A Q }/ { v } + 16

Hence,

A Q ( { 1 }/ { u } - { 1 }/ { v } ) = 16

...(i)
From Statement A:
In this case let us assume that the accident happens at point B Following a similar method as mentioned above we get:
BQ

( { 1 } /{ u } - { 1 } /{ v } ) = 21

( A Q + 10 ) ( { 1 } /{ u } - { 1 }/ { v } ) = 21

...(ii)
From (i) and (ii):
AQ = 32 km and hence, PQ = 30 + 32 = 62 km
From Statement B:
In this case let us assume that the accident happens at point C. Following a similar method as mentioned above we get:

\CQ( { 1 }/ { u } - { 1 }/ { v } ) = 20 ( \ { 1 } /{ u } - { 1 }/ { v } ) = 12

...(iii)
From (i) and (iii):

A Q = { 80 }/ { 3 } { \km }

and hence,

{ \PQ } = 30 + { 80 }/ { 3 } = { 170 }/ { 3 } { \km }

So the question can be answered by using either of the statements alone.

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