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CAT Exam Model Paper 4 with solutions for free online practice

Question : 59 of 60

Marks: +1, -0

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

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

= \frac{PQ}{v} = \frac{(PA + AQ)}{v}

Total time taken by the train due to accident

= \frac{PA}{v} + \frac{AQ}{U} = \frac{PQ}{v} + 16 = \frac{PA}{v} + \frac{AQ}{v} + 16

Hence,

AQ \left( \frac{1}{u} - \frac{1}{v} \right) = 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:

\left( \frac{1}{u} - \frac{1}{v} \right) = 21

(AQ + 10) \left( \frac{1}{u} - \frac{1}{v} \right) = 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 \left( \frac{1}{u} - \frac{1}{v} \right) = 20 \left( \frac{1}{u} - \frac{1}{v} \right) = 12

...(iii)

From (i) and (iii):

AQ = \frac{80}{3} \text{ km}

and hence,

PQ = 30 + \frac{80}{3} = \frac{170}{3} \text{ km}

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

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