CAT Exam Model Paper 4 with solutions for free online practice

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 =

PQ

v

=

(PA+AQ)

v

Total time taken by the train due to accident
=

PA

v

+

AQ

U

=

PQ

v

+16=

PA

v

+

AQ

v

+16
Hence, AQ(

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
or (AQ+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):
AQ=

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.