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# Trains

## 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

## TRAINS SET 4

Q.1 A train passes a pole on the platform in 3sec & the platform in 8sec. If the length of the platform is 120m. Find the length of the train ?A) 68mB) 69mC) 71mD) 72mAns. DShortcut:120/ (8-3) * 3120/5 * 3=72m Q.2 Two trains of length 100m & 80m run on parallel lines of rails. When running in the same direction faster train passes the slower train in 18sec but when they are running in opposite direction with the same speed as earlier they pass each other in 9 sec. Find the speed of each train ?A) Faster train:15m/sec , Slower train:5m/secB) Faster train:5m/sec , Slower train:15m/secC) Faster train:12m/sec , Slower train:4m/secD) Faster train:4m/sec , Slower train:12m/secAns. AShortcut:Faster train:Sum of length/2 * sum of time/product of timei.e (100+80/2) * (18+9 /18*9)=15m/secSlower train:Sum of length/2 * Difference of time / Product of time(100+80/2) * (18-9/18*9)=5m/sec Q.3 Without stoppage a train covers certain distance at an average speed of 80km/hr but with the stoppages it covers same distance at an average speed of 60 km/hr. How much time per hour does the train stop ?A) 15 minB) 16minC) 17minD) 18minAns. AShortcutTime=Difference in speed/Speed without stoppageOr 80-60/80 =1/5 hrsOr 15min Q.4 At a Railway Office , a passenger was told that a train for Delhi had left 15 min ago but after every 45 min. a train leaves for Delhi. Next train will leave at 8:30 pm. At what time was this information given to the passanger ? A) 8:05 pm B) 8:15 pm C) 7:45 pm D) 8:00 pm Ans. D 8:30 – 45 min. + 15 min= 8:00 pm Q.5 Running at a speed of 60 km per hour, a train passed through 1.5 km long tunnel in two minutes. What is the length of train ? A) 1500 m B) 250 m C) 500 m D) 1000 m Ans. C Let length of train be 1 metreSpeed of the train = 60 km/hr= 60 * 1000=60000 m/hrLength of tunnel = 1.5 km = 1500 m Time taken by train = 2 min. = 1/30 hrTime = Distance / Speed1/30 = 1+1500/60000l = 500 m

## TRAINS SET 3

Q.1 A train 110m long running with a speed of 60km/hr. In what time will it pass a man who is walking at 6km/hr ?A) 7 1/3 secB) 6 1/3 secC) 5 1/3 secD) 4 1/3 secAns. A Q.2 Two trains 130m & 120m in length are running in the same direction at 70km/hr & 52km/hr. In what time they be clear of each other from the moment they meet ?A) 50 secB) 51 secC) 52 secD) 53 secAns. AD=130+120=250mS=70-52=18km/hrOr 18*5/18=5m/secOr T=250/5=50sec Q.3 A train travelling 25km/hr leaves Delhi at 9:00 am & another train travelling 35km/hr start at 2 pm in the same direction. How many kilometres from Delhi will they be together ?A) 437 ½kmB) 438 1/2kmC) 439 1/2kmD) 440 1/2kmAns. AShortcut:S1*S2* Difference of time/Difference of speed25*35/35-25 * 5= 437 1/2km Q.4 Two trains for Delhi leave Jaipur at 8:30 am & 9 am & travel at 60 & 75 km/hr. How many km from Jaipur will the two trains meet ?A) 150kmB) 151kmC) 152kmD) 153kmAns. AShortcut:Product/Difference * Difference of time60*75/ 75-60 * (9-8:30)½ * 60*75/15=150km Q. 5 A train passes by a stationary man standing on the platform in 7 sec. & passes by the platform in 28sec. If the length of the platform is 330m, what is the length of train ?A) 110mB) 111mC) 112mD) 113mAns. AShortcut:Length of the platform/Difference in time * time taken to cross stationary man330/28-7 * 7330/21 * 7=110m

## TRAINS SET 2

Q.1 A 60 m long train travels at a uniform speed of 72 km/hr. It passes non-stop along the 600m platform of a wayside station. What is the elapsed time for the train to entire clear the platform ?A) 31 secB) 30 secC) 32 secD) 33 secAns. DConvert speed in meter per second then apply formula. Length is 600+60 Q.2 Train A is 75 m long & travels at a uniform speed of 54 km/hr. Train B is125m long & travels at a uniform speed of 36 km/hr in the direction opposite to that of Train A. If these trains are crossing at a double track stretch, what is the time taken for the two trains to fully clear each other ?A) 10 secB) 8 secC) 7.2 secD) 6.6 secAns. B Q.3 Two trains 121m & 99m in length are running in opposite direction at the speed of 40 & 32 km/hr. In what time will they be completely clear of each other from the moment they meet ?A) 11 secB) 12 secC) 13 secD) 14 secAns. AD= 121+99=220mS=40+32= 72*5/18Or T=220/20=11sec Q.4 Two trains start from Delhi & Chandigarh & move towards each other at speed 80 & 90 km/hr. At their meeting point it is found that the train from Chandigarh has travelled 40 km more than the train coming from Delhi. Find the distance between Delhi & Chandigarh ?A) 660B) 670C) 680D) 690Ans. CShortcut:Sum of speed/Difference of speed*distance80+90/80-90*40=680 Q. 5 A train 100m long takes 6sec to cross a man walking at 5 km/hr in a direction opposite to that of the train. Find the speed of train ?A) 54B) 55C) 56D) 57Ans. BShortcut:Speed=5+x km/hrOr 5+x*5/18m/secT=100/(5+x)*5/18=61800/25+5x=6300=25+x(we have got 300 since,1800/6)On solving, we getX=55

## TRAINS SET 1

Q.1 There are 3 trains from Mumbai to Ahmedabad and 7 trains from Ahmedabad to Kutch. In how many ways can Jethalal reach Kutch? A) 18 ways B) 19 ways C) 20 ways D) 21 ways Ans. D From Mumbai to A’bad, Jethalal can go in 3 ways. (Because there are three train, he can pick anyone)Similarly From A’bad to Kutch, he can go in 7 ways.Total ways: simple multiplication =3 ways x 7 ways =21 ways Jethalal can reach Kutch. Q.2 A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original speed of the train in km/hr? A) 24 B) 33 C) 42 D) 66Ans. CLet the original speed of the train in km/hr.Then as per question,T1 +t2 =63/x+72/x+63= 63(x+6) +72x/ x(x+6)X(x+6)=21(x+6)+24xX2+6x = 21x + 126 +24xX2+6x-45x-126=0X2-39-126 =0Thus on solving, we get(x-42) (x+3)=0Therefore, x=42 Ans. Q.3 A train which travels at the uniform rate of 10m a second leaves Madras for Arconum at 7:00 am. At what distance from Madras will it meet a train which leaves Arconum for Madras at 7:20 am & travels 1/3rd faster than the former does, the distance from Madras to Arconum being 68 km ?A) 36 km B) 47 kmC) 38 kmD) 42 kmAns. AS1= 10*18/5 = 36km/hrS2 = 36+36/3 = 48 km/hrThus, Difference in time = T1 – T2 = 7 am – 7:20 am = -1/3 hrTherefore distance of meeting point from Madras,= 36+ [68-48 ( -1/3 ) / 36+48 ]=36 [68+16 / 36+48 ]= 36km/hr Q.4 Suppose the telegraph poles on a railroad are 50 metres apart , how many will be passed by a car in 4hrs if the speed of the train is 45 km/hr ?A) 3814B) 4221C) 3211D) 3601Ans. DTotal distance covered by the train = 4*45 = 180kmTherefore, in the distance of 180 km , there will be :180000 / 50 + 1 = 3601 poles Q.5 A train travels at a certain average speed for a distance of 63 km. Thereafter it travels a distance of 72 km with an average speed of 6 km/hr more than the original speed. Total time taken to complete the journey is 3 hours. What is the original average speed of the train ?A) 48 km/hrB) 36 km/hrC) 54 km/hrD) 42 km/hrAns. D