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Two cyclists are travelling at a speed of 3 km/h and 10 km/h around a circular track. What is the ratio of a number of meeting points that would meet on that track if they travel in the same direction first and in the opposite direction next?

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Important Questions on Arithmetic

HARD
CAT
IMPORTANT
Quantitative Aptitude for the CAT>Chapter 2 - Arithmetic>Practice Exercises>Q 32
Two trains going on a parallel line in opposite directions take 10 s to cross each other. But if they are going in the same direction, the longer train crosses the shorter train in 30 s. If the length of the longer train is decreased by 50%, the time taken to cross the shorter train while going in the same direction decreases by 8 s. Find the time taken by the longer train to cross a tunnel twice its length, if the difference between the length of the trains is 25 m?
MEDIUM
CAT
IMPORTANT
Quantitative Aptitude for the CAT>Chapter 2 - Arithmetic>Practice Exercises>Q 33
A runner, Ajay runs twice on a circular track at a uniform speed. Vijay start at the same time as Ajay and after Vijay has completed one lap, he stops and Sanjay starts and completes the second lap at a uniform speed. It is given that they start the race exactly at 2:30 pm and the track is 500 m is circumference. Sanjay runs at a speed of 5 km/h greater than that of Vijay and Ajay's speed is 2 km/h greater than that of Vijay. When does Ajay finish the second lap, if Sanjay also finishes at the same time?
HARD
CAT
IMPORTANT
Quantitative Aptitude for the CAT>Chapter 2 - Arithmetic>Practice Exercises>Q 34
A man travels 1200 km from A to B by air, train, and ship. The distance travelled by ship is twice the distance traveled by train. The average speed of the aircraft is twice the overall speed and the time he was on the ship was thrice the time he was on the train. If the man travels 10 h by train out of the total travel time of 50 h, then what is the total distance covered by the ship?
MEDIUM
CAT
IMPORTANT
Quantitative Aptitude for the CAT>Chapter 2 - Arithmetic>Practice Exercises>Q 35
Three friends Rupesh, Nishit, and Vijay planned to race with each other on their bikes. Rupesh has a lot of riding experience, while Nishit had just learned how to ride. The race seemed unfair. Therefore, they decided that the excellent biker Rupesh will form a team with Nishit. They would bike against the other rider Vijay, each riding half the total distance of 50 km. Also, Nishit can ride only half as fast as Vijay and Rupesh travels four times as faster as Nishit. What is the ratio of the time taken by the winner to that of the looser?
MEDIUM
CAT
IMPORTANT
Quantitative Aptitude for the CAT>Chapter 2 - Arithmetic>Practice Exercises>Q 43
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.
MEDIUM
CAT
IMPORTANT
Quantitative Aptitude for the CAT>Chapter 2 - Arithmetic>Practice Exercises>Q 44
Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed of x km/h from Lucknow towards Patna. After 3 h, Sharat leaves at the speed of (x+10)km/h from Lucknow towards Patna. If x and the number of hours taken to meet after Sharat starts are integers, how much distance can Mayank cover before they meet?
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IMPORTANT
Quantitative Aptitude for the CAT>Chapter 2 - Arithmetic>Practice Exercises>Q 45
Two champion swimmers start a two-length swimming race at the same time, but from the opposite ends of the pool. They swim at constant but different speeds. They first pass at a point 18.5 m from the deep end. Having completed one length, each swimmer takes a rest at the edge of the pool for 45 s. After setting off on the return length, the swimmers pass for the second time just 10.5 m from the shallow end. Therefore, the length of the pool is:
HARD
CAT
IMPORTANT
Quantitative Aptitude for the CAT>Chapter 2 - Arithmetic>Practice Exercises>Q 46
A tortoise lays eggs on the beach and goes back to the sea where its mate is waiting. One way to reach the mate is going down 12 km on a straight line perpendicular to the sea, turning 90° and swimming for 5 km on a straight line. On its way down to the sea, the tortoise can cut the water at any point. The speed of the tortoise on land is 1 km/h and in water is 2 km/h. If the tortoise takes the described route, at what distance from the point where it had laid the eggs will the tortoise cut the water if the total time taken is 12 h?