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Q.

An aeroplane left 30 minutes later than its scheduled time; and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hour from its usual speed. What will be its usual speed?


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a

550 km/hr  

b

650 km/hr  

c

850 km/hr  

d

750 km/hr   

answer is D.

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Detailed Solution

Given,
Total distance= 90 km .
Time=30 minutes less time when its speed = 250km/hr   more than the original speed.
Considering the speed of the aeroplane as xkm/hr   and the distance covered= 1500 km in t   hours.
Substituting distance=1500, speed= x   and time= t   in the equation
x= 1500 t  ,
We know that,
30 minutes = 1 2  hours   Now again substituting distance=1500, speed= x+250   and time= t− 1 2   in the equation speed= distance time  ,
⇒x+250= 1500 t−1 2 ⇒x+250= 1500 2t−1 2 ⇒x+250= 3000 2t−1  
Substituting x  = 1500 t   in the equation x+250= 3000 2t−1   ,
⇒ 1500 t +250= 3000 2t−1 ⇒ 1500+250t t = 3000 2t−1 ⇒ 1500+250t 2t−1 =3000t ⇒3000t−1500+500 t 2 −250t=3000t  
⇒−1500+500 t 2 −250t=0 ⇒2 t 2 −t−6=0 ⇒2 t 2 −4t+3t−6=0 ⇒2t t−2 +3 t−2 =0   ⇒ t−2 2t+3 =0 ⇒(t−2)=0 ⇒t=2 ⇒2t+3=0 ⇒t=− 3 2  
Since time cannot be negative, we take the positive value of t.
Substituting t=2 in the equation x= 1500 t  ,
⇒x= 1500 2 ⇒x=750 km/hr  
Thus the original speed of the aeroplane will be 750 km/hr  .
Therefore the correct option is 4.
 
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