Q.1.Train A leaves from P to Q. Half an hour later train B leaves for P from Q. Two hours after A had started, the trains meet. A has covered 50 % more distance than train B when they meet. What is the ratio of the speeds of train A to train B?
a) 6 : 5
b) 5 : 6
c) 9 : 8
d) 8 : 9
Sol : Option C Explanation: Let speed of A is x and speed of B is y. ∴ Distance covered by A in 2 hrs = 2x and distance covered by B in 1.5 hrs = 1.5y. Also 2x = 1.5(1.5y) ⇒ x : y = 9 : 8.
Q.2. Train A leaves Mumbai for Pune at 5:30 a.m. and reaches Pune at 9:30 a.m. Train B leaves Pune for Mumbai at 7:30 a.m. and reaches Mumbai at 13:30 hrs. At what time will these two trains meet?
a) 7:42 a.m.
b) 8:42 a.m.
c) 9:12 a.m.
d) 8:48 a.m.
Sol : Option B Explanation: Train A takes 4 hrs to complete its journey and train B takes 6 hrs to complete its journey. Let the total journey = D. Speed of train A = D/4 and speed of train B = D/6. Distance covered by train A in 2 hrs = D/4 × 2 = D/2. ∴ Remaining distance = D/2 ∴ time taken to meet = = 1 hr 12 min. ∴ Trains will meet at 7.30 + 1 hr12 min. = 8.42 A.M.
Q.3. A train moves at a speed, which is 50% more than the speed of a car. Both start from the point P simultaneously and arrive at a point Q, 120 km away from P at the same time. While on the way, however, the train lost about half an hour while taking halt at the stations. The speed of the car is
a) 120 kmph
b) 75 kmph
c) 80 kmph
d) 60 kmph
Sol : Option C Explanation: Let the speed of the car be x km/hr. ∴ Speed of the train = x + 50% of x = 3x/2 km/hr ∴ 2/3x × 120 + 30/60 = 120/x ⇒ x = 80 km/hr
Q.4.A man is walking at a speed of 15 km per hour. After every kilometre, he takes rest for 3 minutes. How much time will he take to cover a distance of 4 km?
a) 35 minutes
b) 25 minutes
c) 30 minutes
d) 45 minutes
Sol : Option B Explanation: Speed = 15 km/hr. Total distance to be covered = 4 km. Time taken to cover 1 km = 4 min. Hence total time taken = 4 + 3 + 4 + 3 + 4 + 3 + 4 = 25 min
Q.5.A train traveling at the speed of 80 kmph leaves Ambala at 10.30 a.m. and another train traveling at the speed of 95 kmph at 1.30 p.m. leaves Ambala, travelling in the same direction. After how many km from Ambala will they be together?
a) 1760 km
b) 1280 km
c) 1520 km
Sol : Option C Explanation: Distance traveled by 1st train in 3 hrs. = 80 × 3 = 240 km. They are in same direction. ∴ Relative speed = 95 – 80 = 15 km/hr. Time taken to meet = 240/15 = 16 hrs. ∴ Distance from Bombay = 16 × 95 = 1520 km
Q.6.A man covers a certain distance on a toy train. If the train moved 4 km/hr faster, it would have taken 30 minutes less. If it moved 2 km/hr slower, it would have taken 20 minutes more. Find the distance.
b) 60 km
c) 50 km
d) 72 km
Sol : Option B Explanation: Let the distance be D km. Speed of the train be x km / hr and normal time is t hrs. ∴ D / x + 4 = t – 30/60 → D/x + 4 = t - 1/2 Also D /(x –2) = t + 20/60 → D/(x-2) = t + 1/3. Also D = tx. Solving these 3 equations, we get D = 60 km.
Q7.Normally it takes 3 hours for a train to run from A to B. One day, due to a minor trouble the train had to reduce the speed by 12 km/hr and so it took ¾ of an hour more than usual. What is the distance from A to B?
a) 240 km
b) 160 km
c) 150 km
d) 180 km
Sol : Option D Explanation: Normal time = 3 hrs. Increased time = 3 + ¾ = 15 / 4 hours. Let the distance from A to B is D. Speed = S D/S = 3….(I) D/(S -12) =15/4….(II). Solving both equations, we get → D = 180 km.
Q8.Two men undertake to drive a distance of 54 km. The first performs the journey at 8 km/hr. The second, starting half an hour later, arrives 15 minutes sooner. Find the approximate ratio of the speeds of the first to the second person.
a) 7 : 8
b) 6 : 7
c) 9 : 8
d) 8 : 9
Sol : Option D Explanation: Distance to be covered = 54 km. Speed of 1st = 8 km/hr. ∴Time taken by 1st person = 54/8 = 6 ¾ hrs. Hence time taken by 2nd person = 6 ¾ – ½ – 15/60 = 6hrs. ∴ their timing ratio = 27/4 : 6 → 9 : 8. Hence ratio of their speeds = 8 : 9.
Q9.Prateek decides to go on a trip to Matheran along with his girlfriend. They start on his YBX and go by the newly opened Pune Mumbai expressway. At Khopoli, they have to get off the expressway and go the remaining distance on a smaller road. The total distance that Prateek covered was 170 km. His average speed on the expressway was 100 km/hr and off it was 50 km/hr. If the total journey took 2 hours, find the length of the journey that was undertaken on the expressway.
a) 140 km
b) 160 km
c) 150 km
d) 180 km
Sol : Option A Explanation: Let the length of the journey be x, so x / 100 + (170 – x) / 50 = 2. Solving we get x = 140 km.
Q10.It takes ten hours for a 800 km journey, if 200 km is done by Bike and the rest by Electric car. It takes 60 minutes more, if 300 km is done by bike and the rest by Electric car. The ratio of the speed of the Bike to the speed of Electric car is
a) 1 : 2
b) 3 : 2
c) 4 : 5
d) 5 : 3
Sol : Option B Explanation: Let speed of the bike be x km/hr. Let speed of the electric car be y km/hr ∴ 200/x + 600/y = 10 ∴ 300/x + 500/y = 11 → 600/x + 1800/y = 30 …….(1) 600/x + 1000/y = 22……(2) → 800/y = 8 → y = 100, x = 50. ∴ Required ratio = 50 : 100 = 1 : 2