Q-1. A car goes 20 miles on a gallon of gas driving at 60 miles/h. If the car is driven at 75 miles/h, it goes as far as 70%. How many gallons of gas will be required to travel 210 miles/h?
Q-2. A 200-m-long train passes a 350-m-long platform in 5 s. If a man is walking at a speed of 4 m/s along the track and the train is 100 m away from him, how much time will it take to reach the man?
Q-3. There are two clocks. One of them gains two min in 12 h and another one loses two min in 36 h. Both are set right at noon on Tuesday. What will be the correct time when both of them show the same time the next time?
Q-4. Magadh Express and Vikramshila Express run between Patna and New Delhi. Every night each of these trains leaves Patna for Delhi. Similarly, every night each of the trains leaves Delhi for Patna. The train journey lasts 36 h and the trains are identical in all aspects. If the train that leaves at the night is like the one that arrived in the morning, what is the minimum number of trains required?
Q-5. There are two swimmers A and B who start swimming towards each other from opposite banks of the lake. They meet at a point 900 ft. from one shore for the first time. They cross each other, touch the opposite bank and return. They meet each other again at a distance of 300 ft. from the other shore. What is the width of the lake?
Q-6. Vinit’s rowing at a speed of 4 km/h in still water. He has to reach a destination that is 130 km downstream of a river. The river flows at a speed of 2 km/h but due to tides every 2 h, the velocity doubles and then after another 2 h, it halves. If Vinit starts at the change of the tide when the river was flowing at 2 km/h, then after how much time will he reach his destination?
Q-7. A person starts writing natural numbers, starting from 1, on a blackboard, at the rate of 60 digits per min. At the same time, another person begins to erase the digits from 1 onwards, at the rate of 40 digits per min. Find the difference between the leftmost digit and the rightmost digit on the blackboard immediately after 1 h.
Q-8. Two friends Manoj and Sagar start running simultaneously in an opposite direction on a circular track of the length 2100 m with a speed of 7 m/s and 3 m/s, respectively. With every meeting, they exchange their speed and they meet for a total of 10 times. How much distance did Sagar cover in total?
Q-9. A rabbit, a tortoise, and a mongoose decide to run a closed-circuit race. If the rabbit overtakes the mongoose two times per round, with the second overtake being at the starting point and the mongoose overtakes the tortoise four times per round, the fourth overtake being at the starting point, then find the ratio of the speed of the rabbit to that of the tortoise.
Q-10. Directions: There are two cities Nagpur and Pune along a straight line 120 km apart. A and B start at the same time from Nagpur and Pune, respectively, with speeds of 40 km/h and 60 km/h. They travel towards each other, and after they meet for the first time, they reverse directions and also interchange their speeds. After reaching their respective starting points, they reverse their directions and start proceeding toward each other again. How many hours from the beginning do they meet for the second time?
Q-11. Directions: A train started at 9:00 am from station X with a speed of 72 km/h. After 2 h, another train started from station Y toward X with a speed of 90 km/h. The two trains are expected to cross each other at 1:30 pm. Owing to a signal problem arising at noon, the speed of each of them was reduced by the same quantity and they crossed each other at 4:30 pm. What is the new speed of the train that started from station X?
Q-12. Ram and Rahim left Bombay simultaneously towards Pune. The speed of Ram is 15 km/h and the speed of Rahim is 12 km/h. Half an hour later, Mohan started from Bombay towards Pune on the same road in the same direction. After some time, he overtook Rahim, and 90 mins further, he overtook Ram. What is Mohan’s speed?
Q-13. In a certain race, the winner beats the other six contestants by 10, 20, 30, 40, 50, 60 m, respectively. Find by what distance the third runner-up beats the fourth runner-up if he was 11.11 m ahead of the fourth runner-up when the first runner-up finished the race.
Q-14. A building had two floors. There were 90 steps from the first floor to the second floor. An escalator was moving up from the first floor to the second floor. Ram took nine seconds to walk from the first floor to the second floor on it. He took 45 seconds to return to the first floor on it. Find the time he would have taken to return if the escalator had been switched off. (in seconds) _____ (TITA)
Q-15. An escalator was moving up from floor X to floor Y. It had 120 steps. Anil took 24 seconds to walk up on it. If his speed doubled and that of the escalator tripled, he would have taken only ten seconds to walk up on it. Find the time he would take to go from floor Y to floor X by the escalator. (in seconds) _____ (TITA)
Q-16. Flight A leaves city X at 6:00 a.m. and reaches city Y at 8:30 a.m. Flight B leaves city Y at 3:00 p.m. and reaches city X at 10:30 p.m. Both flights fly non-stop between X and Y and all times mentioned are local times. If flight A travels at 600 km/hr and flight B travels at 400 km/hr, find the distance between city X and city Y (in km).
Q-17. A car travelled a distance of 900 km. It developed an engine problem after travelling for some distance. It travelled the remaining distance at 3/5th of its speed. It reached 2 hours late. If the engine problem had developed after it had travelled for another 150 km, it would have reached 1 hour earlier than the time it reached. Find the distance it travelled without any problem and its speed over that part of the journey. (In km, in km/h).
Q-18. Vijay and his girlfriend started on a boat from a point on a river and began to row upstream. After rowing for two hours, Vijay stopped the boat. He wanted to hand over a flower to his girlfriend but it slipped from his hand into the river and floated downstream. They rowed upstream for two more hours and then turned back. They caught up with the flower, at a point 6 km downstream of the point at which it fell into the river. Find the speed (in km/hr) of the stream.
Q-19. A train travelling at 36 km/hr takes 48 seconds to cross a bridge. It then crosses a man cycling at 9 km/hr in the same direction in 20 seconds. Find the length of the bridge. (in metres) _____ (TITA)
Q-20. In a 500 m race, A beats B by 40 m. In a 1000 m race, B beats C by 40 m. If A beats C by 14 6 seconds in a 500 m race, find the time taken (in minutes) by B to run 2.4 km. _____ (TITA)
Q-21. Three runners A, B and C run around a circular track at different speeds. They start at the same point, but while A and B run clockwise, C runs anticlockwise. All 3 go around the track several times. It is found that between A and B, the faster overtakes the slower at 3 different points. A and C cross each other at 7 different points and B and C cross each other at 10 different points. What could be the ratio of the speeds of A, B and C?
Q-22. A boat P travels 40 km upstream from point A to point B in 10 hours and from point B to point A downstream in 5 hours. Another boat Q can travel from point A to point C, 30 km upstream, in 5 hours. At 10 am, P starts from A and goes towards B. At the same time, Q starts from C and goes towards A. At what time will they meet each other?
Q-23. A, B and C take part in a race over a distance of d metres at a uniform speed. If A can beat B by 20 metres, B can beat C by 10 metres and A can beat C by 28 metres, then what is the value of d?
Q-24. The distance between TCY Ludhiana and TCY Jalandhar is less than 100 km. Aman started from TCY Ludhiana and after 10 hours, he came across a milestone showing the distance between it and TCY Ludhiana. He moved further and 2 hrs later, he came across another milestone showing the distance, exactly the reverse of that shown by the previous milestone. What is Aman's speed?
Q-25. Directions: Kanpur Express departs from Delhi at 10 a.m. for Kanpur at an average speed of 60 kmph. At noon, Rajdhani Express left Delhi on the same route. At 2 p.m., Shatabdi Express left Delhi on the same route. All three trains meet together at 8 p.m. before reaching Kanpur. (Assume there is no stop in between) If Shatabdi Express reaches Kanpur at 10 p.m., at what time will Kanpur Express reach Kanpur?
Q-26. Train A and Train B are running on parallel tracks with speeds of 72 kmph and 54 kmph, respectively. If they move in the same direction, Mr. Ravi, who sits in the slower train, observes that the faster train passes him in 18 seconds. If they move in opposite directions, both trains pass each other in 24 seconds. Find the length of the slower train.