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# CAT 2018 [SLOT 1] Quant Question with Solution 32

Question:
The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is

1. 4
2. 6
3. 5
4. 3
Show Answer
Correct Answer: 3

Let the time taken by Partha to cover 60 km be x hours.

As per the condition, Narayan will cover 60 km in x-4 hours.

Therefore, Speed of Partha = $\frac{60}{x}$

And Speed of Narayan = $\frac{60}{x-4}$

It is also given that Partha reaches the mid-point of A and B two hours before Narayan reaches B. Hence,

=> $\frac{30}{\frac{60}{x}} + 2 = \frac{60}{\frac{60}{(x-4)}}$

$\frac{x}{2} + 2 = x-4$

$\frac{x+4}{2}=x-4$

$x+4=2x-8$

$x=12$

OR Partha will take 12 hours to cross 60 km.

=> Speed of Partha = $\frac{60}{12}=5$ Kmph.

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