A130 km/hr
B125 km/hr
C115 km/hr
D120 km/hr
Answer:
D. 120 km/hr
Read Explanation:
Total distance to be covered = total length of both the trains = 152. 5 + 157.5 = 310 m ⇒ Total time taken = 9.3 sec ⇒ Speed = distance/time = (310/9.3) m/sec = (310/9.3) × (18/5) = 120 km/hr ∴ The combined speed of the two trains every hour would then be 120 km/hr. Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 4 A train having a length of 500 m passes through a tunnel of 1000 m in 1 minute. What is the speed of the train in Km/hr? 75 Km/hr 90 Km/hr 87 Km/hr 96 Km/hr Answer (Detailed Solution Below) Option 2 : 90 Km/hr Problem on Trains MCQ Question 4 Detailed Solution Let the speed of the train be x m/s. Given length of the train = 500 m Length of the tunnel = 1000 m Time taken to pass the tunnel = 1 minute = 60 seconds ∴ x = (500 + 1000) ÷ 60 x = 25 m/s Speed of the train in km/hr = Speed of the train = 90 km/hr. Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 5 Two trains are going from Bangalore to Chennai with a speed of 80km/hr and 100km/hr. If the train with slower speed starts 1 hour before then find the time taken by the second train to catch the 1st train. 6 hours 5 hours 4 hours 8 hours Answer (Detailed Solution Below) Option 3 : 4 hours Problem on Trains MCQ Question 5 Detailed Solution GIVEN: Speed of trains are 80 km/hr and 100 km/hr and lower speed train start 1 hour earlier FORMULA USED: Distance = Time × Speed CALCULATION: Speed of trains are 80 km/hr and 100 km/hr and slower speed train start 1 hour earlier Distance covered by slower train in 1 hour = 80 × 1 = 80 km Relative speed = 100 - 80 = 20 km/hr So the time is taken by the faster train to cross the slower train = 80/20 = 4 hours ∴ Time taken by 2nd train to catch the 1st train is 4 hours Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 6 A train crossed a 110 m long platform in 13.5 seconds and a 205 m long platform in 18.25 seconds. What was the speed of the train? 72 km/h 66 km/h 69 km/h 75 km/h Answer (Detailed Solution Below) Option 1 : 72 km/h Problem on Trains MCQ Question 6 Detailed Solution Let the length of train be x m. ⇒ Speed of train = (length of platform + length of train)/time According to question, ⇒ (110 + x)/ 13.5 = (205 + x)/18.25 ⇒ (110 + x)/2.7 = (205 + x)/3.65 ⇒ 401.5 + 3.65x = 553.5 + 2.7x ⇒ 0.95x = 152 ⇒ x = 160 ⇒ Speed of train = (110 + 160)/13.5 = 20 m/sec = 20 × (18/5) = 72 km/hr Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 7 A train met with an accident 720km away from station A. It completed remaining journey at 75% of the previous speed and reached station B, 4.5 hr late. If accident taken place 120 km further, it would have been only 4 hrs late. Then, what is the normal speed of the train? 80 km/hr 60 km/hr 50 km/hr 90 km/hr Answer (Detailed Solution Below) Option 1 : 80 km/hr Problem on Trains MCQ Question 7 Detailed Solution Concept Used: Time = Distance/Speed Calculation: Suppose the normal speed of the train is 4x km/hr and the speed after the accident will be 3x km/hr. The difference in the time of (4.5 hr – 4 hr) = 30 min is because of 120 km. According to question – ⇒ 120/3x – 120/4x = 30/60 ⇒ 120(4 – 3)/12x = ½ ⇒ 120/12x = ½ ⇒ 10/x = ½ ⇒ x = 20 ∴ The normal speed of the train will be 4x = 80 km/hr. Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 8 A cyclist was riding alongside a railway track at a steady speed of 12 km/hr. A train running at a speed of 84 km/hr coming from behind the cyclist crosses him in 13.5 seconds. What is the length of the train? 240 m 270 m 320 m 360 m Answer (Detailed Solution Below) Option 2 : 270 m Problem on Trains MCQ Question 8 Detailed Solution ∵ The train and cyclist are moving in the same direction, Relative speed = 84 – 12 = 72 km/hr. = 72 × 5/18 = 20 m/sec. Now, time taken to cross cyclist = Length of train/relative speed ⇒ 13.5 = Length of train/20 ∴ Length of train = 20 × 13.5 = 270 m Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 9 Two trains are moving at 56 kmph and 29 kmph, respectively in the same direction. The faster train crosses a person sitting in the slower train in 16s. What is the length of the faster train? 100 m 120 m 124 m Data is insufficient Answer (Detailed Solution Below) Option 2 : 120 m Problem on Trains MCQ Question 9 Detailed Solution Given: Speed of faster train = 56 kmph Speed of slower train = 29 kmph Time taken to cross = 16 sec Calculations: Relative speed of the trains ⇒ 56 – 29 ⇒ 27 kmph ⇒ 27 × 5/18 m/sec ⇒ 15/2 m/sec Now, length of the faster train ⇒ Relative Speed × Time ⇒ 15/2 × 16 ⇒ 120 m The length of the faster train is 120 m. As the faster train is crossing a person sitting in the slower train then the faster train has to cover a distance equal to its own length with relative speed. ∴ Time in which faster train crosses the man sitting in slower train = Relative speed/Lenght of Faster train Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 10 A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? 120 m 240 m 300 m None of these Answer (Detailed Solution Below) Option 2 : 240 m Problem on Trains MCQ Question 10 Detailed Solution Given: A train passes the platform in 36 seconds The train passes a man in 20 seconds The speed of the train is 54km/h Formula used: Speed = Distance/Time To convert km/h into m/s we multiply by 5/18 Calculation: Convert speed into m/s ⇒ 54 × 5/18 = 15 m/s The length of the train is ⇒ 15 × 20 = 300 metre Distance covered in 36 seconds ⇒ 36 × 15 = 540 metre The length of the platform is ⇒ 540 - 300 = 240 metre ∴ The length of the platform is 240 meter Convert speed into m/s ⇒ 54 × 5/18 = 15 m/s Time taken to cover platform is ⇒ 36 - 20 = 16 seconds Length of the platform is ⇒ 15 × 16 = 240 metre ∴ The length of the platform is 240 meter Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 11 A train of length 340 m passes a man travelling in the opposite direction in 18 s. If the train travels with a speed of 63 kmph, what is the speed of the man? 2 kmph 3 kmph 4 kmph 5 kmph Answer (Detailed Solution Below) Option 4 : 5 kmph Problem on Trains MCQ Question 11 Detailed Solution Speed of the train = 63 kmph Length of train = 340 m Time taken by train to pass the man = 18 s Relative speed m/s Relative speed kmph Since, they travel in the opposite direction Relative speed = Speed of train + Speed of man Speed of man = Relative speed - Speed of train = 68 - 63 = 5 kmph Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 12 Two trains are running on opposite tracks between stations A and B. After crossing each other they take 4 hr and 9 hr respectively to reach their destination. If speed of first train is 54 kmph, find the speed of second train. 18 kmph 36 kmph 44 kmph 28 kmph Answer (Detailed Solution Below) Option 2 : 36 kmph Problem on Trains MCQ Question 12 Detailed Solution Given: Two trains are running on opposite tracks between stations A and B. After crossing each other they take 4 hr and 9 hr respectively to reach their destination. Speed of first train is 54 kmph. Formula used: After crossing each other, if time taken by 2 trains is T1 and T2 resp. then, S1/S2 = √T2/√T1 where, S1 and S2 are speeds of first and second train respectively Calculation: We have, T1 = 4hr, T2 = 9hr, S1 = 54 kmph ⇒ 54/ S2 = √[9/4] = 3/2 ⇒ S2 = 54 × 2 × 1/3 = 36 kmph ⇒ Speed of second train = 36 kmph Alternate Method Let the speed of the second train be 'x' kmph Also, time taken to cross each other = √(T1 × T2) = √(9 × 4) = 6 hrs Total distance = 54 × 6 + x × 6 = x × 9 + 54 × 4 ⇒ 9x - 3x = 54 × (6 - 2) ⇒ 6x = 216 ⇒ x = 36 kmph = Speed of second train Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 13 The time taken for the tail end of a train to cross a pole is 53 seconds. If the length of the train is 110 m and speed of the train is 36 km/hr, find the initial distance of the pole from the front end of the train. 420 m 530 m 640 m 1798 m Answer (Detailed Solution Below) Option 1 : 420 m Problem on Trains MCQ Question 13 Detailed Solution ⇒ Speed = Distance/time ⇒ Speed of train = 36 × (5/18) = 10m/s ⇒ Distance covered in 53 seconds = 10 × 53 = 530 m ⇒ Length of train = 110m ∴ The initial distance of the pole from the front end of the train = 530 – 110 = 420 m. Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 14 A train 1350 m long takes 135 seconds to cross a man running at a speed of 5kmph in a direction same to that of the train. What is the speed of the train? 60 km/h 41 km/h 52 km/h 86 km/h Answer (Detailed Solution Below) Option 2 : 41 km/h Problem on Trains MCQ Question 14 Detailed Solution Given: The length of the train = 1350 m Speed of men = 5 km/h Time to cross the men = 135 seconds Calculation: Let the speed of the train be x km/h Relative speed = (x - 5) km/h ⇒ (x - 5) = ( 1350 × 18)/(135 × 5 ) ⇒ X - 5 = 36 ⇒ X = 36 + 5 = 41 km/h Hence, 41 Km/h is the speed of train Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 15 A train running at 45 kmph crosses a man running at 9 kmph in same direction in 20 seconds. Find the length of train. 150 meter 200 meter 350 meter 250 meter Answer (Detailed Solution Below) Option 2 : 200 meter Problem on Trains MCQ Question 15 Detailed Solution Given: A train running at 45 kmph crosses a man running at 9 kmph in same direction in 20 seconds. Formula used: Time = Distance/ Speed Here, Distance = Length of train When running in same direction ∴ Relative Speed = Speed of train - Speed of man Calculation: Relative Speed = (45 – 9) kmph = 36 kmph = 36 × 5/18 meter per sec. = 10 meter per sec. ∴ Time = Length of train/Relative Speed ⇒ 20 = Length of train/10 ⇒ Length of train = 20 sec. × 10 meter per sec. = 200 meter ∴ The length of train is 200 m Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 16 Two trains A and B are moving at speeds of 54 kmph and 90 kmph respectively. The lengths of train A and train B are 350 m and 400 m respectively. The difference in the time taken by both the trains to cross the platform of a certain length is 14 seconds. Find the length of the platform. 250 m 280 m 300 m 270 m Answer (Detailed Solution Below) Option 1 : 250 m Problem on Trains MCQ Question 16 Detailed Solution Given: Speed of train A = 54 kmph Speed of train B = 90 kmph Length of train A = 350 m Length of train B = 400 m The difference in the time taken by both trains to cross the platform of a certain length =14 seconds Concept used: Speed of train = (length of train + length of the platform)/time 1 kmph = 5/18 m/s Calculation: Let the length of the platform be L m. Speed of train A = 54 × 5/18 = 15 m/s Speed of train B = 90 × 5/18 = 25 m/s ⇒ (L + 350)/15 – (L + 400)/25 = 14 ⇒ 25L + 8750 – 15L – 6000 = 5250 ⇒ 10L = 2500 ⇒ L = 250 m ∴ The length of the platform is 250 m. Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 17 A train passes two persons moving at the speeds of 26 m/s and 42 m/s in the opposite direction to that of the train in 9 sec and 7 sec respectively. The length of the train is 504 m 449 m 479 m 443 m Answer (Detailed Solution Below) Option 1 : 504 m Problem on Trains MCQ Question 17 Detailed Solution Given: A train passes two persons moving at the speeds 26 m/s and 42 m/s in the opposite direction to that of the train in 9 sec and 7 sec respectively. Formula used: Distance = speed × time Calculation: Let the speed of train be ST, Distance = length of train(L) Speed(S1) of first person be 26 m/s, Speed(2) of second person be 42 m/s Relative speed, person moving opposite direction, First person passes ⇒ (ST + S1) = L/9 ⇒ ST = (L/9) – 26 ----(1) Second person passes ⇒ (ST + S2) = L/7 ⇒ ST = (L/7) – 42 ----(2) Substitute the value of ST in equation (1) ⇒ L/9 – 26 = L/7 – 42 ⇒ L/7 – L/9 = 16 ⇒ L = 16 × 63/2 ⇒ L = 504 m ∴ The length of the train is 504 m. Formula used: Length of train = (S2 – S1)T1 × T2/(T1 – T2) ⇒ (42 – 26)× 9 × 7/(9 – 7) ⇒ 504 m. ∴ The length of the train is 504 m. Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 18 Find the time taken by a train 450 m long to cross a platform twice its length at a speed of 81 km/h. 70 sec 60 sec 40 sec 50 sec Answer (Detailed Solution Below) Option 2 : 60 sec Problem on Trains MCQ Question 18 Detailed Solution GIVEN: Length of train = 450 m Speed of train = 81 km/h Length of platform = 2 × length of train CONCEPT: Distance traveled by train to cross a platform = (length of train + length of platform) FORMULA USED: Speed = Distance/Time CALCULATION: Platform's length = 2 × 450 = 900 m Total distance = 450 + 900 = 1350 m Speed (m/s) = 81 × 5/18 = 45/2 m/s Time = 1350/(45/2) Time = (1350 × 2)/45 = 60 sec ∴ Time taken is 60 sec To convert km/h into m/s multiply by 5/18. Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 19 A train crosses a pole in 12 sec, and a bridge of length 170 m in 36 sec. Then the speed of the train is: 30.75 km/h 25.5 km/h 32.45 km/h 10.8 km/h Answer (Detailed Solution Below) Option 2 : 25.5 km/h Problem on Trains MCQ Question 19 Detailed Solution Shortcut Trick If train cross its length in 12 seconds and 170 m bridge in (36 - 12 = 24) seconds. Speed of train = [170/24] × [18/5] = 25.5 km/hr Alternate Method Let the length of the train be x m. As we know, Speed = Distance/time Speed = x/12 ---(1) Speed = (x + 170)/36 ---(2) Frome equation (1) and equation (2) x/12 = (x + 170)/36 ⇒ 3x = x + 170 ⇒ 2x = 170 ⇒ x = 170/2 ⇒ x = 85 m From equation (1) Speed = 85/12 × (18/5) km/hr ∴ Speed = 25.5 km/hr Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students Problem on Trains MCQ Question 20 A train travelling at 36 km/h crosses a pole in 25 seconds. How much time (in seconds) will it take to cross a bridge 250 m long? 56 72 48 50 Answer (Detailed Solution Below) Option 4 : 50 Problem on Trains MCQ Question 20 Detailed Solution Given : Speed of train = 36 km/h Time taken to cross a pole = 25 seconds Length of bridge = 250 m Formula used : Distance = speed × time Solution : Speed of train = 36 × (5/18) ⇒ Speed of train = 10 m/s ⇒ Time taken = 25 seconds ⇒ Length of train = 25 × 10 ⇒ Length of train = 250 m ⇒ Length of bridge = 250 m ⇒ Total length = length of tran + length of bridge ⇒ Total length = 250 + 250 ⇒ Total length = 500 m ⇒ Time taken to cross the bridge = 500/10 ∴ the time taken to cross the bridge is 50 second. Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Live Masterclass Daily Live MasterClasses Practice Question Bank Practice Question Bank Mock Tests & Quizzes Mock Tests & Quizzes Trusted by 2,46,90,791+ Students