A car travels from P to Q at a constant speed. If the speed were increased by 10 km/hr, it would have taken 1 hour less to cover the distance. It would have taken 45 minutes less if the speed was further increased by 10 km/hr. What is the distance between the two cities?

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350 km

420 km

425 km

465 km

answer is B.

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Detailed Solution

Concept- The time to move from P to Q at a constant speed is

Where x is the distance and y is the velocity. Now, if the speed increases by 10 km / h, the time will be

and less than an hour, so

. Simplify it to create an equation. Follow the same procedure to create another equation when the speed is further increased by 10 km / h.
Time taken can be calculated as

Given,
If the speed were increased by 10 km/hr, time taken will be be

It would have taken less than an hour to cover the distance. If the speed is increased by another 10km / h, it will be reduced by another 45 minutes.
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In equation 2 put equation 1
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By putting y=60 in the equation (i) we get:
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Hence, the correct answer is option (2).

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