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Q.

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km / h more, it would have taken 30 minutes less for the journey. Find the original speed of the train.


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a

11 km/h

b

15 km/h

c

30 km/h

d

45 km/h 

answer is D.

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Detailed Solution

Given,
A train covers a distance of 90 km at a uniform speed and if the speed is increased by 15 km/h, it takes 30 minutes less.
Total distance = 90 km
Assume the original speed of the train to be x km/h.
Then the increased speed will be (x+15) km/h.
Time taken t 1   by the train to cover a distance of 90 km   with a speed of x km/h  
 Time  =  Distance   Speed  ⇒ t 1 = 90 x ……..1   Time taken t 2   by the train to cover a distance of 90 km   with a speed of (x+15)km/h  
Time  =  Distance   Speed  ⇒ t 2 = 90 x+15 ……..2   Therefore, according to the given conditions
90 x − 90 x+15 = 30 60 ……(3)[ From (1) and (2)]  
Obtain the quadratic equation using equation (3)
⇒ 90 x − 90 x+15 = 1 2 ⇒ 90x+1350−90x x(x+15) = 1 2 ⇒ 1350 x 2 +15x = 1 2 ⇒ x 2 +15x−2700 =0  
⇒ x 2 +60x−45x−2700=0 ⇒x(x+60)−45(x+60)=0 ⇒(x+60)(x−45)=0  
Either x+60=0   or x−45=0   Therefore, x=−60   or x=45   Since x represents speed, hence it cannot be negative.
Therefore, the original speed of the train is 45 km/hr.
Hence, the correct option is 4.
 
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