Previous Year CAT Questions for Arithmetic

1. CAT 2024 QA Slot 1 | Arithmetic - Time, Speed & Distance CAT Question

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 Anil, in km per hour, is

(a)
16
(b)
12
(c)
18
(d)
14

2. CAT 2024 QA Slot 2 | Arithmetic - Time, Speed & Distance CAT Question

A bus starts at 9 am and follows a fixed route every day. One day, it traveled at a constant speed of 60 km per hour 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 per hour to reach just on time. The scheduled arrival time of the bus is

(a)
7 pm
(b)
9 pm
(c)
10:30 pm
(d)
7:30 pm

3. CAT 2024 QA Slot 3 | Arithmetic - Time, Speed & Distance CAT Question

A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is

(a)
640
(b)
780
(c)
800
(d)
720

4. CAT 2023 QA Slot 1 | Arithmetic - Time, Speed & Distance CAT Question

Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of x km till then, where x is a whole number and is palindromic, i.e., x remains unchanged when its digits are reversed. At the end of the trip, the car had travelled a total of 26862 kms till then, this number again being palindromic. If Brishti never drove at more than 110 kmph, then the greatest possible average speed at which she drove during the rip, in kmph was?

(a)
110
(b)
80
(c)
90
(d)
100

5. CAT 2023 QA Slot 1 | Arithmetic - Time, Speed & Distance CAT Question

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 travelled at a speed of 54 km/h, then the distance, in km, between town A and town B is

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Answer: 972

Video Explanation

Text Explanation :

After meeting they take 6 and 24 hours to reach opposite end.
∴ Time taken to meet = $\sqrt{6 \times 24}$ = √144 = 12 hours.

⇒ X takes a total of 12 + 6 = 18 hours to reach from A to B.

∴ Distance between A and B = distance travelled by X in 18 hours = 18 × 54 = 972 kms.

Hence, 972.

Concept:

Time taken to reach other end after meeting

6. CAT 2023 QA Slot 2 | Arithmetic - Time, Speed & Distance CAT Question

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 should drive so that all the three cross each other at the same time, is

(a)
67.2
(b)
58.8
(c)
61.6
(d)
64.4

Answer: Option C

Video Explanation

Text Explanation :

Speed of
Ravi = 40 × 5/18 = 100/9 m/s and
Ashok = 50 × 5/18 = 250/18 m/s

Time taken for them to meet = $\frac{225}{\frac{100}{9} + \frac{250}{18}}$ = $\frac{225 \times 18}{450}$ = 9 secs.

⇒ Vijay and Ravi should also meet in 9 secs.
∴ 9 = $\frac{54}{V - \frac{100}{9}}$

⇒ 9V - 100 = 54

⇒ 9V = 154

⇒ V = 154/9 m/s = 154/9 × 18/5 kmph = 61.6 kmph

Hence, option (c).

Concept:

Relative Speed

7. CAT 2023 QA Slot 3 | Arithmetic - Time, Speed & Distance CAT Question

A boat takes 2 hours to travel downstream a river 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 return to port B. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is?

(a)
3(3 + √5)
(b)
3(√5 - 1)
(c)
3(3 - √5)
(d)
12(√5 - 2)

Answer: Option C

Video Explanation

Text Explanation :

Let the speeds of river, faster and slower boats be r, f and s km/hr respectively and distance between A and B be 12 kms.

For Faster boat:
⇒ f + r = 12/2 = 6 ...(1)
⇒ f - r = 12/3 = 4 ...(2)

(1) - (2)
⇒ 2r = 6 - 4 = 2
⇒ r = 1

For Slower boat:
⇒ $\frac{12}{s - 1}$ + $\frac{12}{s + 1}$ = 6

⇒ $\frac{12 \times 2 s}{s^{2} - {(1)}^{2}}$ = 6

⇒ s² - 1 = 4s

⇒ s² - 4s - 1 = 0

∴ s = $\frac{4 \pm \sqrt{16 + 4}}{2}$ = 2 ± √5 = 2 + √5 [negative value of s is rejected]

Now, time taken by the slower boat to go from A to B

= $\frac{12}{(2 + \sqrt{5}) + 1}$ = $\frac{12}{(3 + \sqrt{5})}$ = $\frac{12 (3 - \sqrt{5})}{9 - 5}$ = 3(3 - √5).

Hence, option (c).

Concept: Boats & Streams

8. CAT 2022 QA Slot 1 | Arithmetic - Time, Speed & Distance CAT Question

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 train B to travel from station Y to station X is

(a)
12
(b)
15
(c)
10
(d)
6

9. CAT 2022 QA Slot 2 | Arithmetic - Time, Speed & Distance CAT Question

Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is

(a)
18
(b)
24
(c)
12
(d)
20

10. CAT 2022 QA Slot 3 | Arithmetic - Time, Speed & Distance CAT Question

Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is

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11. CAT 2022 QA Slot 3 | Arithmetic - Time, Speed & Distance CAT Question

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 distance travelled, in km, by the slower car when it meets the other car while traveling towards each other, is

(a)
90
(b)
120
(c)
100
(d)
150

12. CAT 2021 QA Slot 1 | Arithmetic - Time, Speed & Distance CAT Question

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m, is

(a)
180
(b)
184
(c)
190
(d)
192

13. CAT 2021 QA Slot 2 | Arithmetic - Time, Speed & Distance CAT Question

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 length of train A to that of train B is

(a)
2 : 1
(b)
3 : 2
(c)
2 : 3
(d)
5 : 3

Answer: Option B

Video Explanation

Text Explanation :

Let the lengths of trains A and B be ‘A’ and ‘B’ and their speeds be ‘a’ and ‘b’ respectively.

Time taken for front end of A to cross rear end of B = 46 seconds

⇒ 46 = $\frac{B}{a + b}$

⇒ B = 46a + 46b …(1)

Total time taken for rear ends of the two train to cross each other = (46 + 69) = 115 seconds

⇒ 115 = $\frac{A + B}{a + b}$

⇒ A + B = 115a + 115b …(2)

(2) - (1)

⇒ A = 69a + 69b …(3)

Now, $\frac{A}{B}$ = $\frac{69 (a + b)}{46 (a + b)}$ = $\frac{69}{46}$ = $\frac{3}{2}$

Hence, option (b).

Concept:

Trains

14. CAT 2021 QA Slot 3 | Arithmetic - Time, Speed & Distance CAT Question

Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in 45 minutes, Amal completes exactly 3 more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after 3 minutes. The number of rounds Mira walks in one hour is

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15. CAT 2020 QA Slot 1 | Arithmetic - Time, Speed & Distance CAT Question

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

(a)
75
(b)
82
(c)
87
(d)
78

Answer: Option B

Video Explanation

Text Explanation :

Let the speed and length of train be ‘s’ m/s and ‘t’ m respectively.

Speeds of two persons is 2 kmph and 4 kmph i.e., 5/9 m/s and 10/9 m/s

Train passes the first person in 90 seconds.

∴ $\frac{t}{s - \frac{5}{9}}$ = 90

⇒ t = 90s – 50 …(1)

Train passes the second person in 100 seconds.

∴ $\frac{t}{s - \frac{10}{9}}$ = 100

⇒ t = 100s – 1000/9 …(2)

(1) = (2)

⇒ 90s – 50 = 100s – 1000/9

⇒ s = 55/9 m/s and t = 500 m

∴ Time taken to cross an electric pole = $\frac{500}{55 / 9}$ = $\frac{4500}{55}$ = $\frac{900}{11}$ = 81.81 ≈ 82 seconds.

Hence, option (b).

Concept:

Trains

16. CAT 2020 QA Slot 1 | Arithmetic - Time, Speed & Distance CAT Question

A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

(a)
100
(b)
90
(c)
70
(d)
80

17. CAT 2020 QA Slot 1 | Arithmetic - Time, Speed & Distance CAT Question

Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8 km/hr, and at 9:40 am if he travels at 15 km/hr. Leaving home at 9:10 am, at what speed, in km/hr, must he travel so as to reach office exactly at 10 am?

(a)
13
(b)
14
(c)
11
(d)
12

Answer: Option D

Video Explanation

Text Explanation :

Let the distance between home and office be d kms.

∴ $\frac{d}{8} - \frac{d}{15} = \frac{35}{60} = \frac{7}{12}$

⇒ d = 10 kms

If he leaves home at 9:10 a.m. and reaches office at 10 a.m., i.e., time taken = 50 minutes = 5/6 hours

∴ Required speed = $\frac{10}{5 / 6}$ = 12 kmph.

Hence, option (d).

18. CAT 2020 QA Slot 1 | Arithmetic - Time, Speed & Distance CAT Question

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 which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

(a)
58
(b)
61
(c)
67
(d)
50

Answer: Option C

Video Explanation

Text Explanation :

Since the train travelled at 1/3rd of its speed, it will take thrice the usual time.

Hence, if the normal time taken for train is t minutes, now it will take 3t minutes.

∴ 3t – t = 30

⇒ t = 15 minutes.

While coming back train travels at usual speed for 5 minutes and then takes 4 minutes break.

∴ If the train has to come back at scheduled time, it needs to cover the remaining distance in (15 – 5 – 4 =) 6 minutes. Train usually takes 10 minutes to travel this distance.

∴ The time reduced to 6/10 = 3/5th hence speed should become 5/3 times.

∴ % increase = $\frac{\frac{5}{3} - 1}{1}$ × 100 = 66.66% ≈ 67%

Hence, option (c).

19. CAT 2020 QA Slot 2 | Arithmetic - Time, Speed & Distance CAT Question

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

(a)
550
(b)
450
(c)
475
(d)
500

Answer: Option B

Video Explanation

Text Explanation :

Let their speeds be a, b and c respectively and the length of the race be D.

Car A beats car B by 45 kms

∴ $\frac{a}{b} = \frac{D}{D - 45}$ …(1)

Car B beats car C by 50 kms

∴ $\frac{b}{c} = \frac{D}{D - 50}$ …(2)

Car A beats car C by 90 kms

∴ $\frac{a}{c} = \frac{D}{D - 90}$ …(3)

(1) × (2) = (3)

⇒ $\frac{D}{D - 45} \times \frac{D}{D - 50} = \frac{D}{D - 90}$

⇒ $\frac{D}{(D - 45) (D - 50)} = \frac{1}{D - 90}$

⇒ D² – 95D + 2250 = D² – 90D

⇒ 5D = 2250

⇒ D = 450

Hence, option (b).

Concept:

Linear Race

20. CAT 2020 QA Slot 2 | Arithmetic - Time, Speed & Distance CAT Question

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, then the ratio of Ram's speed to Rahim's speed is

(a)
√2
(b)
2√2
(c)
1/2
(d)
2

21. CAT 2020 QA Slot 2 | Arithmetic - Time, Speed & Distance CAT Question

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 Rahim again for the first time is

(a)
3
(b)
5
(c)
4
(d)
2

Answer: Option A

Video Explanation

Text Explanation :

Time taken by Ram to reach the starting point A = $\frac{2 \times π \times 0.1}{15} = \frac{π}{75}$

Time taken by Rahim to reach the starting point A = $\frac{2 \times π \times 0.02}{5} = \frac{π}{125}$

Both of them will meet only at A since they are running in different circles which meet at A.

Both of them will reach the starting point after LCM $[\frac{π}{75}, \frac{π}{125}]$ = $\frac{π}{25}$

∴ Number of rounds completed by Ram when both of them meet again = $\frac{\frac{π}{25}}{\frac{π}{75}}$ = 3

Hence, (a).

22. CAT 2020 QA Slot 2 | Arithmetic - Time, Speed & Distance CAT Question

The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1 while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to that taken by train 2 in travelling from A to C is

(a)
4 : 1
(b)
7 : 5
(c)
5 : 7
(d)
1 : 4

Answer: Option C

Video Explanation

Text Explanation :

Let the distance from A to B = d and that from B to C = 3d.

Speed of train T₁ = s from A to B and 2s from B to C.

Total time taken by T₁ = $\frac{d}{s} + \frac{3 d}{2 s} = \frac{5 d}{2 s}$

Speed of train T₂ = 2s from A to B and s from B to C.

Total time taken by T₂ = $\frac{d}{2 s} + \frac{3 d}{s} = \frac{7 d}{2 s}$

∴ Ratio of time taken by T₁ and T₂ = $\frac{5 d}{2 s} : \frac{7 d}{2 s}$ = 5 : 7

Hence, option (c).

23. CAT 2020 QA Slot 3 | Arithmetic - Time, Speed & Distance CAT Question

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

(a)
11:45 a.m.
(b)
11 a.m.
(c)
10:45 a.m.
(d)
11:20 a.m.

24. CAT 2020 QA Slot 3 | Arithmetic - Time, Speed & Distance CAT Question

Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is

(a)
26
(b)
28
(c)
29
(d)
27

Answer: Option B

Video Explanation

Text Explanation :

Let the distance from home to office be d kms.

∴ $\frac{d}{35} - \frac{d}{40} = \frac{6}{60}$

⇒ d = 28 kms.

∴ Normal time taken = $\frac{28}{40}$ = 0.7 hour = 42 minutes.

Now, she covers 2/3^rd of this distance in 1/3rd time i.e., in 14 minutes.

She now takes rest for 8 minutes.

∴ Time elapsed = 14 + 8 = 22 minutes.

Time remaining = 20 minutes.

In 20 minutes she needs to travel 1/3^rd of the distance i.e., 28/3 kms.

∴ Time taken = $\frac{28 / 3}{20 / 60}$ = 28 kmph.

Hence, option (b).

25. CAT 2020 QA Slot 3 | Arithmetic - Time, Speed & Distance CAT Question

Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

(a)
4.6
(b)
4.2
(c)
5.2
(d)
4.8

Arithmetic - Time, Speed & Distance - Previous Year CAT/MBA Questions

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