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Q.

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. What is the speed of the train?


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a

50 km/h

b

40 km/h

c

35 km/h

d

30 km/h 

answer is B.

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Detailed Solution

Given that a train travels 360 km at a uniform speed.
Also, if the speed had been 5 km/h more, it would have taken 1 hour less for the same journey.
Let the speed of train be n km/h.
We know,
Time= Distance Speed  
Let the time taken by train to cover distance of 360 km = 360 n   hour.
Speed of the train increased by 5 km = n + 5.
Let the new time taken by train to cover distance of 360 km = 360 n+5   hour.
As the train time decreased by 1 hour, if the speed is increased, the difference of the time taken before and after increase of speed is 1.
Now,
360 n − 360 n+5 =1  
Form the quadratic equation.
Take L.C.M n and (n+5), we get
⇒ 360 n − 360 n+5 =1 ⇒ 360(n+5)−360n n(n+5) =1 ⇒ 360n+1800−360n n 2 +5n =1 ⇒1800= n 2 +5n ⇒ n 2 +5n−1800=0  
⇒ n 2 +45n−40n−1800=0 ⇒n(n+45)−40(n+45)=0 ⇒(n+45)(n−40)=0 ⇒n+45 or n−40=0 ⇒n=−45 or n=40  
We got our two speeds of train as n=-45 and n=40.
But the speed of the train can never be negative.
So, the speed of the train is n=40 km/h.
Therefore, the correct option is 2.
 
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