A plane left 30 min later than the scheduled time and in order to reach the destination 1500km away ...........

Quantitative Aptitude ( CCS) Time & distance

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

750

850

700

900

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Explanation:

Let the usual time taken by the aeroplane = x km/hr
Distance to the destination = 1500 km
Case (i)
Speed = Distance / Time = (1500 / x) Hrs
Case (iI)
Time taken by the aeroplane = (x - 1/2) Hrs
Distance to the destination = 1500 km
Speed = Distance / Time = 1500 / (x - 1/2) Hrs
Increased speed = 250 km/hr
⇒ [1500 / (x - 1/2)] - [1500 / x] = 250
⇒ 1/(2x² - x) = 1/6
⇒ 2x² - x = 6
⇒ (x - 2)(2x + 3) = 0
⇒ x = 2 or -3/2
Since, the time can not be negative,
The usual time taken by the aeroplane = 2 hrs
and the usual speed = (1500 / 2) = 750 km/hr.