## TRAINS SET 5

Q.1 If a train maintains an average speed of 40km an hour, it arrives at its destination punctually. If however average speed is 35 km an hour, it arrives 15 min. late. Find the length of the train ? A) 70 B) 30 C) 40 D) 80 Ans. A Shortcut:Product of speed/difference of speed*time i.e. 40*35/40-35*15/60we have divided given time by 60 since it is given in min. therefore, 1400/5*15/60=70 Q.2 Two trains A and B started at the same time from Delhi with speed of 60 km/h and 80 km/h respectively. They did not stop anywhere up to Kanpur. Train ‘A’ reached Kanpur 40 minutes after train ‘B’ reached. What is the distance between Delhi and Kanpur? A) 120 km B) 140 km C) 160 km D) 180 km Ans. C Shortcut:Product / difference * timeOr 60*80 / 80-60 * 40/60=160 Q.3 The speed of two trains is 30 m/s and 35 m/s. They cross each other in 6 sec, if they travel in opposite direction. How much time does it take for the faster train to overtake the slower train? A) 30 sec B) 35 sec C) 60 sec D) 78 sec Ans. D Given = 6 sec (where d is the sum of the lengths of trains).d =390mTime = Answer = 78 sec Q.4 A journey of 192 km takes 2 hours less by a fast train than by a slow train.If the average speed of the slow train be 16 kmph less that of the fast train, What is the average speed of the faster train. A) 32kmph B) 16 Kmph C) 12 Kmph D) 48 Kmph Ans. D speed of faster train = xspeed of slower train = yGiven,(1) from 1st statement of problem: 192/x = (192/y) – 2 …………..eq. 1(2) from 2nd statement of problem: y = x – 16 ………………….eq.2replacig eq.2 in eq.1 we get,192/x = (192/x-16) – 2 ……………….eq.3solving,x = 48 and y = 32 (ignoring the -ve solution for x in quadratic eq.3)Therefore, average speed of faster train = 48 Kmph