A train covers 400 km at a uniform speed. If the speed had been 10 km/h, it would have taken 2 hours less for the same journey. What is the usual time taken ( in hours) by it to complete the journey?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 10.
Let the speed of the train be s
Time is taken by train = 400/s
Now, the increased speed of the train be (s + 10)
Now, Time taken by train = 400/(s + 10)
According to the question;
Difference between time taken = 2 hours
⇒ 400/s - 400/(s + 10) = 2
⇒ 1/s - 1/(s + 10) = 2/400
⇒ (s + 10 - s)/s(s + 10) = 1/200
⇒ 200(s + 10 - s) = s(s + 10)
⇒ 2000 = s2 + 10s
⇒ s2 + 10s - 2000 = 0
⇒ s2 + 50s - 40s - 2000 = 0
⇒ s(s + 50) - 40(s + 50) = 0
⇒ s = -50, 40
So, The speed of train = 40 km/hr
Time taken by train = 400/40 = 10 hours