Question 1

CAT 2025 Slot 3: Rahul starts on his journey at 5pm at a constant speed so that he reaches his destination at 11pm same day . However , on his way , he stops for 20 minutes and after that, increases his speed by 3 km per hour to reach on time. If he had to stop for 10 minutes more , he would have

Accepted Answer

Answer: B · 15. Let Rahul's initial speed be V km/h. The total distance D is D = V × 6. When he stops for 20mins (6-⅓ = 17/3) , t - l time 6V = (v × t) + (v + 3) × (17/3 - t) On solving we have v/3 = 17 - 3t , v = 51 - 9t —- I When he stops for 30 mins (6-½) = 11/2 6v = (v × t) + (v + 5) (11/2 - t) On solving V/2 = 55/2 - 5t , v = 55 - 10t —--- II On solving I and II , we have t = 4 , then  v = 15km/hr Thus option 2 is the answer

Question 2

CAT 2025 Slot 2: Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes 48 minutes more to row 14 km upstream than to row the same distance downstream. If Rita starts from a certain location in the river, and retur

Accepted Answer

Answer: 8. Concept of upstream and Downstream: Sneha’s speed = 6 km/h, let river speed = x km/h Time difference: 14/(6-x) - 14/(6+x) = 0.8 , x = 1 km/h Rita’s effective speed Upstream = 5 - 1 = 4 km/h Downstream = 5 + 1 = 6 km/h Time to go and return = 100 min = 5/3 h d/4 + d/6 = 5/3 , d = 4 km Total distance: Total distance = 4 + 4 = 8 km Answer: 8 km

Question 3

CAT 2024 Slot 1: Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of

Accepted Answer

Answer: A · 12. Speed of Anil - MathJax Solution Speed of Anil Distance between A and B = 45 km They meet after $ 1.5 $ hours Let Anil's speed be $ a $ km/h and Sunil's speed be $ s $ km/h Since they meet after 1.5 hours: $ 1.5a + 1.5s = 45 \Rightarrow a + s = 30 \quad \text{(Equation 1)} $ It's also given: Anil takes 1 hour 15 minutes more than Sunil to reach destination. Time taken by Anil after meeting: $ \frac{1.5s}{a} $ Time taken by Sunil after meeting: $ \frac{1.5a}{s} $ Given: $ \frac{1.5s}{a} = \frac{1.5a}{s} + 1.25 $ Multiply both sides by $ a \cdot s $: \( 1.5s^2 = 1.5a^2 + 1.25as \

Question 4

CAT 2023 Slot 2: Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay s

Accepted Answer

Answer: A · 61.6. Ans 1

Question 5

CAT 2023 Slot 1: Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town B while Surbhi takes 24 hours to reach town A. If Arvind traveled at a speed of 54 km/h, then

Accepted Answer

Answer: D · 972 km. The total distance between town A and B, given the speeds and time taken, is 972 km.

Question 6

CAT 2022 Slot 3: Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distan

Accepted Answer

Answer: C · 90. Let the distance between the 2 cars be D km. Let the speeds of the two cars be ‘a’ and ‘b’ respectively and a > b. Case I) Cars are moving in the opposite direction (towards each other) Relative speed = a + b Time taken = 1.5 hrs Case II) Cars are moving in the same direction (Car A chasing Car B) Relative speed = a - b Time taken = 10.5 hrs In both the cases the distance between the cars is the same, ‘D’. But the time taken is in the ratio 1.5 : 10.5 or 1 : 7 Therefore, the speeds will be in the ratio 7 : 1 a + b = 7(a - b) 8b = 6a 3a = 4b Substituting b = 60 kmph, We get, a = 80 kmph. D = (a

Question 7

CAT 2022 Slot 3: Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km, the triangle formed by the new positions of the two ships and the port

Accepted Answer

Answer: B · 12. Let us denote the port by P, the slower ship by S. the faster ship by F. Triangle APB is right-angled, We know that angle APB is 60 degrees, because triangle SFA is equilateral. The right angle must be at point B, because angle PAB is less than 60 degrees. sin(30) = 1/2=BP/AP BP = 0.5(AP) = 8 BF = FP - BP = 24 - 8 = 16 That mean, the faster ship is twice as fast as the slower one. So, when the faster ship reaches the Port covering 24 km, the slower ship covers only 12 km and has remaining 12 km left to cover.

Question 8

CAT 2022 Slot 1: Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by t

Accepted Answer

Answer: A · 15. Let the meeting point of the two trains between stations X and Y be M. Let the time taken to reach M from X by train A be ‘t’ minutes. Since the two trains start simultaneously, the time taken by train B to reach M from Y will also be ‘t’ minutes. We know that train A completes the entire journey in 10 minutes, so the time taken by train A to travel from M to Y will be ‘10 - t’ minutes. We are told that train B takes 9 minutes to reach X after it meets train A, which means, train B takes 9 minutes to travel from M to X. When two bodies travel equal distances at constant speeds, the ratio of ti

Question 9

CAT 2021 Slot 2: Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to cross eac

Accepted Answer

Answer: D · 3 : 2. Two trains A and B were moving in opposite directions, their speeds being in the ratio of 5 : 3. The speed of train A is 5x. The speed of train B is 3x. Let's assume length of train A and train B are La and Lb The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. So, the distance travelled is Lb. For this, the time taken is 46 sec. Trains took another 69 seconds for the rear ends of the trains to cross each other. So, the distance travelled is La. For this, the time taken is 69 sec. La/5x+3x/Lb/5x+3x =69/46 The relative speed is (5x

Question 10

CAT 2020 Slot 3: A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

Accepted Answer

Answer: B · 11 : 00 am. Now both the trains A and B have 90 - 60 = 30 km to cover between them. The relative speed of the two trains will be 40 + 20 = 60kmph. With a relative speed of 60kmph, the two trains cover 30km in half an hour. Hence the two trains will meet at 11: 00 AM

Question 11

CAT 2020 Slot 2: In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

Accepted Answer

Answer: D · 450. Let the length of the race track be 'x' km. By the time A finishes the race, B lags by 45km. That is, in the same time, while A runs x kms, B runs (x-45) kms Ratio of Speeds of A and B = x/x−45 By the time B finishes the race, C lags by 50km. That is, in the same time, while B runs x kms, C runs (x-50) kms Ratio of Speeds of B and C = x/x−50 By the time A finishes the race, C lags by 90km. That is, in the same time, while A runs x kms, C runs (x-90) kms Ratio of Speeds of A and C = x/x−90 (Ratio of Speeds of A and B) × (Ratio of Speeds of B and C) = (Ratio of Speeds of A and C) x/x−45× /xx−50

Question 12

CAT 2020 Slot 2: Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram and Rahim are walking on track T1 and track T2 at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will make before he meets R

Accepted Answer

Answer: B · 3. R1 = 100m and R2 = 20m Speed of Ram = 15km/hr and Rahim’s speed = 5km/hr Time taken by Ram = 2π(100)/15 Time taken by Rahim = 2π(20)/5 Ratio of the time taken by Ram : Rahim = 5 : 3 After 15 units of time Ram and Rahim will be at starting point and meeting That time ram would have done 3 rounds

Question 13

CAT 2020 Slot 1: A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by whic

Accepted Answer

Answer: B · 67. Let’s take speed of the train to be x and the time taken be t Since speed is reduced to 1/3 rd, New speed = x/3 Since the speed is one-third, time taken will be tripled. T = 3t This 3t is after the scheduled time, So extra 2t = 30 mintues t = 15 minutes Train travels at x km/hr takes 15 minutes and Train travels at x/3 km/hr takes 45 minutes So, the train usually takes 15 minutes to cover the distance. It travels 5 minutes at the usual speed. That is, it travels 1/3 rd of the time at the usual speed. So it covers 1/3 rd of the distance in 5 minutes. To reach it's destination in the on time, th

Question 14

CAT 2020 Slot 1: Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

Accepted Answer

Answer: B · 82. Two person to be A and B A = 2km/hr and B = 4 km/hr Speed of the train = t km/hr Given, Train crosses A in 90 seconds (Length of the train is the distance) t – 2 in 90 seconds and t – 4 in 100 seconds Ratio of speed is opposite to time (t – 2) 90 = (t - 4) 100 Solving t = 22km/hr For A, Speed = t – 2 = 20 km/hr in 90 seconds So travelling at 22 km/hr ----> 90×20/22 ≅ 82

Question 15

CAT 2020 Slot 1: Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8kmph, and at 9:40 am if he travels at 15kmph. Leaving home at 9:10 am, at what speed, in kmph, must he travel so as to reach office exactly at 10:00 am?

Accepted Answer

Answer: A · 12. Speed are 8 km/hr and 15 km/hr So it takes 15t times and 8t times Difference of times = 15t – 8t = 7t 7t = 35 minutes (10:15 min – 9:40 min) t = 5 minutes He takes 75 minutes by travelling at 8 km/hr and 40 minutes if travelled at 15 km/hr He starts at 9 am. So, 9:10 to 10:00 = 50 minutes 15 km/hr = 40 min And at what speed he should travel, so as to reach there within 50 minutes 15×40/50 = 12 km/hr

Question 16

CAT 2019 Slot 2: A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motorcycle leaves A and moves towards B. Forty-five such motorcycles reach B by 11 am. All motorcycles have the same speed. If the cyclist had doubled his speed, how many motorcycles would

Accepted Answer

Answer: C · 15. It is given that the cyclist starts at 10:00 am from A and reaches B at 11:00 am Now, Motorcyclists start every minute from 10:01 am, and 45 such motorcyclists reach B before 11:00 am If they leave one by one every minute, the 45th motorcyclist would have left by 10:45 am to reach B at 11:00 am. Thus, time taken by one motorcyclist to reach B from A = 15 minutes. Now, the cyclist doubles his speed. This means, he reaches B at 10:30 am So, the last motorcyclist should have left A by 10:15 am Thus, 15 motorcyclists would have reached B by the time the cyclist reaches B

Question 17

CAT 2019 Slot 2: John jogs on track A at 6 kmph and Mary jogs on track B at 7.5 kmph. The total length of tracks A and B is 325 metres. While John makes 9 rounds of track A, Mary makes 5 rounds of track B. In how many seconds will Mary make one round of track A?

Accepted Answer

Answer: 48. Let the track length for John be 'a' and for Mary be 'b' So, Distance travelled by John = 9a Distance travelled by Mary = 5b Now, Time taken by John = hours Time taken by Mary = hours We know that Time taken by John = Time taken by Mary = a = b Total track length = 325 meters So, b + b = 325 meters b = 325 meters b = 225 meters a = 100 meters Mary jogs at 7.5 Kmph = 7.5 x So, time taken = = 48 seconds

Question 18

CAT 2019 Slot 2: Two ants A and B start from a point P on a circle at the same time, with A moving clock-wise and B moving anti-clockwise. They meet for the first time at 10:00 am when A has covered 60% of the track. If A returns to P at 10:12 am, then B returns to P at

Accepted Answer

Answer: A · 10:27 am. By the time A and B meet for the first time, A covers 60% of the distance, while B covers 40% of the distance. So, the speeds of A and b are in the ratio 60:40 or 3:2 Hence, the time they take to cover a particular distance will be in the ratio 2:3 We know that A covers 60% of the distance at 10:00 AM and covers 100% of the distance at 10:12 AM. That means A takes 12 minutes to cover 40% of the track. So to cover the entire track he must have taken 12+12+6 = 30 minutes. (because 40% + 40% + 20% = 100%) Since the time taken by A and B to complete the track are in the ratio 2:3, the time taken b

Question 19

CAT 2019 Slot 1: Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least 6 hours, then the highest possible value of the percentage by which the speed

Accepted Answer

Answer: A · 20. The minimum time travelled by Car 1 = 6 hours. Minimum time travelled by Car 2 = 5 hours Now, the time taken can be of any value -> (6,5) (7,6) ...... (1000,999) However, since we want to calculate the highest possible percentage by which speed of car 2 could exceed car 1, we consider the lowest time taken - 6 hours and 5 hours, respectively. Let the distance between the start and finish be 30 Kms (LCM of 6 and 5) So, Car 1 travels at 5 Kmph and Car 2 travels at 6 Kmph Percentage increase in speed by Car 2 = x 100 = x 100 = 20%

Question 20

CAT 2019 Slot 1: In a race of three horses, the first beat the second by 11 metres and the third by 90 metres. If the second beat the third by 80 metres, what was the length, in metres, of the racecourse?

Accepted Answer

Answer: 880. A beats B by 11 meters. When B completes the 11 meters, there is a lead of 80 meters to C So, C must have travelled only 90 - 80 = 10 meters When B travels 11 meters, C travels only 10 meters Ratio of distance travelled by second and third horse are11x and 10 x respectively We know that the second horse beats the third horse by 80 meters. So, Length of the track = Distance travelled by the second horse = 11 x 80 = 880 meters

Question 21

CAT 2019 Slot 1: One can use three different transports which move at 10, 20, and 30 kmph, respectively. To reach from A to B, Amal took each mode of transport 1/3 of his total journey time, while Bimal took each mode of transport 1/3 of the total distance. The percentage by which Bimal’s travel

Accepted Answer

Answer: A · 22. Let the distance be = 60 Kms. So, Bimal travels a distance of 20Kms in each mode and Amal travels 10, 20 and 30 Kms respectively in 1 hour each Time taken by Bimal = Time taken to travel 20 kms in 10 Kmph + Time taken to travel 20 kms in 20 Kmph + Time taken to travel 20 kms in 30 Kmph Time taken by Bimal = 2 + 1 + hours = 3 + hours Extra time taken by Bimal = hour Percentage increase in time = x 100 = x 100 = 22 So, Percentage increase in time = 22

Question 22

CAT 2019 Slot 1: The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While traveling a certain distance, each wheel of A required 5000 more revolutions than each wheel of B. If bicycle B traveled this distance in 45 minutes, then its speed, in km per hour, was

Accepted Answer

Answer: B · 16π. Circumference of A and B are in the ratio 3: 4 So, Ratio of Distance travelled in one revolution by A and B = 3: 4 Since they travel the same distance, Ratio of number of revolutions of A and B = 4: 3 ----- (1) We know that each wheel of A requires 5000 more revolutions than B So, the Ratio of number of revolutions of A and B = (n + 5000): n ------(2) So, comparing (1) and (2) Number of revolutions of A and B are 20000 and 15000 respectively So, we know Bike B does 15000 revolutions in 45 minutes Distance travelled = 2 x π x r x Number of revolutions Speed of Bike B = mph Speed of Bike B = 2 x

Question 23

CAT 2018 Slot 2: Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each c

Accepted Answer

Answer: A · 1 : 4. It is given that points A, P, Q and B lie on the same line such that P, Q and B are 100 km, 200 km and 300 km away from A. Let us draw the diagram first. All of them are on the same straight line and P, Q lie between A and B. Cars 1 and Cars 2 leave A at the same time and move towards B. Simultaneously, Car 3 leaves B and moves towards A. Let us add more details to the diagram. C1 and C2 move towards B and C3 moves towards A. C3 meets C1 at Q and C3 meets C2 at P. Let us assume the speeds of Car 1, 2, and 3 to be C1, C2 and C3 respectively. Car 1 is travelling quicker than Car 2. When Car 1 tr

Question 24

CAT 2018 Slot 2: On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs. The diffe

Accepted Answer

Answer: 50. Given that A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. They meet after one hour or their relative velocity is (a + b)km/hr and their relative distance is 350kms a + b = 35013501 which is equal to 350 kms/hr If they both move towards east, then they meet in 7 hrs. We have to find the difference between their speeds, in km per hour. B is catching upon A, so once again their relative distance will be 350kms. Relative speed = b – a , B travels faster so that it can meet a. ⟹ 350b−a350�−� = 7 ⟹ b - a = 50 km/hr We know that b +

Question 25

CAT 2018 Slot 2: Points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A. Each car travels at a speed of 100 kmph for the first 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km. The distance, in km, b

Accepted Answer

Answer: 5. Given that points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A. Each car travels at a speed of 100 kmph for the first 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km. The Car 1 is 20km away from A and it travels at 100kmph and the time taken is 2010020100 = 1515hr So car 2 is 12 minutes behind car 1. We have to find the distance in km, between car 2 and B when car 1 reaches B. If car 1 reaches B, car 2 will take 12 minutes to reach b. Distance between car 2 and B is 25 × 1515 = 5 kms The dista

Question 26

CAT 2018 Slot 1: The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour,

Accepted Answer

Answer: D · 5. Let Narayanan take X hrs to reach B then Partha would take X + 4 hrs Its given that Partha reaches the mid-point of A and B two hours before Narayan reaches B X+42�+42 = X – 2 => X=8 hrs So, Partha would take 8+4 = 12 hrs to travel 60 Kms at a speed of 60126012 Kmph Speed of Partha = 5 Kmph