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Question

A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.


A

650 km/hr

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B

950 km/hr

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C

850 km/hr

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D

750 km/hr

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Solution

The correct option is D

750 km/hr


Let the usual speed of the plane be x km/hr.

Then, time taken to cover 1500 km with the usual speed

=1500xhrs

Time taken to cover 1500 m with the speed of (x+250)km/hr=1500x+250

1500x=1500x+250+12

1500x1500x+250=12

1500x+1500×2501500xx(x+250)=12

1500×250x2+250x=12

750000=x2+250x

x2+250x750000=0

x2+1000x750x750000=0

x(x+1000)750(x+1000)=0

(x+1000)(x750)=0

x=1000 or, x=750

x=750
[ speed cannot be negative]

Hence, the usual speed of the plane is 750 km/hr


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