# A passenger train takes 1 hour less for a journey of 120 km :

A passenger train takes 1 hour less for a journey of 120 km, if its speed is increase by 10 km/hour from its usual speed. What is its usual speed?
(A) 50 km/hour
(b) 40 km/hour
(c) 35 km/hour
(d) 30 km/hour

Anurag Mishra Professor Asked on 19th February 2016 in

Solution:-
Let the usual speed of a passenger train be X km/hr and time taken by train be Y hr.

Time taken by train with original speed (Y) = 120/X
X Y = 120
X = 120/Y

Train 1 hour less for a journey, if its speed is increase by 10 km/hr.
Then,  (Y + 10) = 120 /(X – 1)
(X – 1) (Y + 10) = 120
X Y + 10 X – Y – 10 = 120

Put the value of X = 120/Y,
Then,  120 Y/Y + 10 x 120/Y – Y – 10 = 120
120 + 1200/Y – Y – 10 = 120
1200  – Y^2  – 10 Y = 0
Y^2 + 10 Y – 1200 = 0
Y^2 + 40 Y – 30 Y – 1200 = 0
Y (Y + 40) – 30 (Y + 40) = 0
(Y – 30) (Y + 40) = 0
Y – 30 = 0
Y = 30

Then, the usual speed of the train is 30 km/hr.

Hence,the correct answer is option (d) 30 km/hr.

Anurag Mishra Professor Answered on 19th February 2016.