Time, Speed and Distance – Level 3 (Advanced)
- IIMwalaBanda
- Aug 1
- 4 min read
1. A bus starts at 9 am and follows a fixed route every day. One day, it traveled at a constant speed of 60 km/h and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it traveled two-thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km/h to reach just on time. The scheduled arrival time of the bus is [CAT 2024, Slot 2]
(a) 7 pm
(b) 9 pm
(c) 10:30 pm
(d) 7:30 pm
2. A boat takes 2 hours to travel downstream from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and back to port B. If the speeds of both boats and the river are constant, the time, in hours, taken by the slower boat to travel from port A to port B is [CAT 2023, Slot 3]
(a) 3(3 + √5)
(b) 3(√5 − 1)
(c) 3(3 − √5)
(d) 12(√5 − 2)
3. Trains A and B start travelling 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. The total time taken, in minutes, by train B to travel from station Y to station X is [CAT 2022, Slot 1]
(a) 12
(b) 15
(c) 10
(d) 6
4. Two ships meet mid-ocean, and then one ship goes south and the other goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one ship is 6 km/h more than the other, the speed, in km/h, of the slower ship is [CAT 2022, Slot 2]
(a) 18
(b) 24
(c) 12
(d) 20
5. 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 each other. The ratio of the length of train A to that of train B is [CAT 2021, Slot 2]
(a) 2:1
(b) 3:2
(c) 2:3
(d) 5:3
6. Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8 km/h, and at 9:40 am if he travels at 15 km/h. Leaving home at 9:10 am, at what speed, in km/h, must he travel so as to reach office exactly at 10 am? [CAT 2020, Slot 1]
(a) 13
(b) 14
(c) 11
(d) 12
7. 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 [CAT 2020, Slot 2]
(a) 550
(b) 450
(c) 475
(d) 500
8. A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, the ratio of Ram's speed to Rahim's speed is [CAT 2020, Slot 2]
(a) √2
(b) 2√2
(c) 1/2
(d) 2
9. 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 walk on track T1 and track T2 at speeds 15 km/h and 5 km/h respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is [CAT 2020, Slot 2]
(a) 3
(b) 5
(c) 4
(d) 2
10. Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/h. She is late by 6 minutes if she drives at 35 km/h. One day, she covers two-thirds of her distance to office in one-third of her usual time, then stops for 8 minutes. The speed, in km/h, at which she should drive the remaining distance to reach office exactly on time is [CAT 2020, Slot 3]
(a) 26
(b) 28
(c) 29
(d) 27
11. Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, going clockwise. If they run at speeds of 15 km/h, 10 km/h, and 8 km/h respectively, how much distance, in km, will Ravi have run when Anil and Sunil meet again for the first time at the starting point? [CAT 2020, Slot 3]
(a) 4.6
(b) 4.2
(c) 5.2
(d) 4.8
Scroll to the bottom for answer key and visit @iimwalabanda YouTube page for video solution
Answer Key
Correct Option | |
Q1 | D (7:30 pm) |
Q2 | C (3(3 − √5)) |
Q3 | B (15) |
Q4 | A (18) |
Q5 | B (3:2) |
Q6 | D (12) |
Q7 | B (450) |
Q8 | D (2) |
Q9 | A (3) |
Q10 | B (28) |
Q11 | D (4.8) |
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