Previous Year OMET Questions for Arithmetic

1. XAT 2020 QADI | Arithmetic - Time, Speed & Distance

Two friends, Ram and Shyam, start at the same point, at the same time. Ram travels straight north at a speed of 10km/hr, while Shyam travels straight east at twice the speed of Ram. After 15 minutes, Shyam messages Ram that he is just passing by a large telephone tower and after another 15 minutes Ram messages Shyam that he is just passing by an old banyan tree. After some more time has elapsed, Ram and Shyam stop. They stop at the same point of time. If the straight-line distance between Ram and Shyam now is 50 km, how far is Shyam from the banyan tree (in km)? (Assume that Ram and Shyam travel on a flat surface.)

A.
20√5 + 5
B.
20√5 - 5
C.
5√21
D.
45
E.
115/3

2. XAT 2020 QADI | Arithmetic - Time, Speed & Distance

A hare and a tortoise run between points O and P located exactly 6 km from each other on a straight line. They start together at O, go straight to P and then return to O along the same line. They run at constant speeds of 12 km/hr and 1 km/hr respectively. Since the tortoise is slower than the hare, the hare shuttles between O and P until the tortoise goes once to P and returns to O. During the run, how many times are the hare and the tortoise separated by an exact distance of 1 km from each other?

A.
40
B.
24
C.
48
D.
42
E.
22

3. IIFT 2019 QA | Arithmetic - Time, Speed & Distance

A motorboat takes the passengers from Rishikesh to Haridwar and back. Both the cities, Rishikesh and Haridwar are located on the banks of River Ganga. During Kumbh Mela, to earn more money, the owner of the motorboat decided to have more trips from Rishikesh to Haridwar and back, so he increased the speed of the motorboat in still water, by 50%. By increasing the speed, he was able to cut down the travel time from Rishikesh to Haridwar and back, by 60%. What is the ratio of the speed of motorboat in still water to that of the speed of river Ganga?

A.
√(11/6)
B.
√11/6
C.
√(3/2)
D.
√3/2

Answer: Option A

Explanation :

Let the speed of boat in still water be ‘b’ and speed of river be ‘r’ and the one-way distance between the two cities be ‘d’.

Time taken initially to go and come back = $\frac{d}{b + r}$ + $\frac{d}{b - r}$

When the speed of boat increases by 50%, time taken to go and come back = $\frac{d}{1.5 b + r}$ + $\frac{d}{1.5 b - r}$

New time taken is 40% of the initial time taken

⇒ $\frac{d}{1.5 b + r} + \frac{d}{1.5 b - r}$ = $\frac{2}{5} [\frac{d}{b + r} + \frac{d}{b - r}]$

⇒ $\frac{3 b}{2.25 b^{2} - r^{2}}$ = $\frac{2}{5} [\frac{2 b}{b^{2} - r^{2}}]$

⇒ 15b² – 15r²= 9b² – 4r²

⇒ 6b² = 11r²

⇒ $\frac{b}{r}$ = $\sqrt{\frac{11}{6}}$

Hence option (a).

4. IIFT 2019 QA | Arithmetic - Time, Speed & Distance

You travel by Delhi Metro everyday from Botanical Garden, Noida to Hauz Khas, Delhi. At Hauz Khas metro station, you use an escalator to get out from the station. The escalator takes 80 seconds. One day, escalator was not working and you walk up the escalator in 50 seconds. How many minutes does it approximately take you to walk down the working escalator?

A.
1.5 minutes
B.
2.2 minutes
C.
2.8 minutes
D.
2.6 minutes

5. XAT 2018 QADI | Arithmetic - Time, Speed & Distance

Every day a person walks at a constant speed, V₁ for 30 minutes. On a particular day, after walking for 10 minutes at V₁, he rested for 5 minutes. He finished the remaining distance of his regular walk at a constant speed, V₂, in another 30 minutes. On that day, find the ratio of V₂ and his average speed (i.e., total distance covered /total time taken including resting time).

A.
1 : 1
B.
1 : 2
C.
2 : 3
D.
2 : 1
E.
None of the above

6. XAT 2018 QADI | Arithmetic - Time, Speed & Distance

A girl travels along a straight line, from point A to B at a constant speed, V₁ meters/sec for T seconds. Next, she travels from point B to C along a straight line, at a constant speed of V₂ meters/sec for another T seconds. BC makes an angle 105° with AB. If CA makes an angle 30° with BC, how much time will she take to travel back from point C to A at a constant speed of V₂ meters/sec, if she travels along a straight line from C to A?

A.
0.5(√3 - 1)T
B.
T
C.
0.5(√3 + 1)T
D.
√3T
E.
None of the above

7. XAT 2017 QADI | Arithmetic - Time, Speed & Distance

Arup and Swarup leave point A at 8 AM to point B. To reach B, they have to walk the first 2 km, then travel 4 km by boat and complete the final 20 km by car. Arup and Swarup walk at a constant speed of 4 km/hr and 5 km/hr respectively. Each rows his boat for 30 minutes. Arup drives his car at a constant speed of 50 km/hr while Swarup drives at 40 km/hr. If no time is wasted in transit, when will they meet again?

A.
at 9:15 am
B.
at 9:18 am
C.
at 9:21 am
D.
at 9:24 am
E.
at 9:30 am

8. IIFT 2017 QA | Arithmetic - Time, Speed & Distance

Ramesh and Sohan start walking away from each other from a point P at an angle of 120°. Ramesh walks at a speed of 3 kmph while Sohan walks at a speed of 4 kmph. What is the distance between them after 90 minutes?

A.
9.89 km
B.
10.56 km
C.
9.12 km
D.
12.42 km

9. XAT 2016 QADI | Arithmetic - Time, Speed & Distance

Pradeep could either walk or drive to office. The time taken to walk to the office is 8 times the driving time. One day, his wife took the car making him walk to office. After walking 1 km, he reached a temple when his wife call to say that he can now take the car. Pradeep figure that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office.

A.
1
B.
7/3
C.
9/7
D.
16/7
E.
16/9

Answer: Option C

Explanation :

Time taken to walk to the office is 8 times the driving time. It means that speed while driving is 8 times the speed while walking.

Let the walking speed be ‘s’ kmph
∴ Driving speed = 8s kmph

Let the distance between home and office be D kms.

Now, time taken to (D – 1) kms is same as time taken to walk 1 km and then drive D kms.

∴ $\frac{D - 1}{s}$ = $\frac{1}{s}$ + $\frac{D}{8 s}$

⇒ 8(D – 1) = 8 + D

⇒ 7D = 16

⇒ D = 16/7

∴ Distance between temple and office = D – 1 = 16/7 - 1 = 9/7

Hence, option (c).

10. XAT 2016 QADI | Arithmetic - Time, Speed & Distance

Study the figure below and answer the question:

Four persons walk from Point A to Point D following different routes. The one following ABCD takes 70 minutes. Another person takes 45 minutes following ABD. The third person takes 30 minutes following route ACD. The last person takes 65 minutes following route ACBD. IF all were to walk at the same speed, how long will it take to go from point B to point C?

A.
10 mins
B.
20 mins
C.
30 mins
D.
40 mins
E.
Cannot be answered as the angles are unknown.

11. IIFT 2016 QA | Arithmetic - Time, Speed & Distance

Shruti and Krishna left Delhi for Noida at the same time. While Shruti was driving her car, Krishna, an environmentalist by profession, was traveling on his bicycle. Having reached Noida, Shruti turned back and met Krishna an hour after they started. Krishna continued his journey to Noida after the meeting, while Shruti turned back and also headed for Noida. Having reached Noida, Shruti again turned back and met Krishna 30 minutes after their first meeting. The time taken by Krishna to cover the distance between Delhi and Noida is

A.
2 hours
B.
2.5 hours
C.
3 hours
D.
None of the above

12. IIFT 2015 QA | Arithmetic - Time, Speed & Distance

A chartered bus carrying office employees travels everyday in two shifts- morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning by:

A.
18% less
B.
30% greater
C.
37.5% greater
D.
50% less

Answer: Option B

Explanation :

Let the bus travels at speed ‘V’km/hr for time ‘T’ hours in the morning.

∴ Distance travelled in the morning = VT km

∴ In the evening, it travels at speed ‘1.5V’km/hr for ‘1.5T’ hours respectively.

∴ Distance travelled in the evening = 1.5V × 1.5T = 2.25VT

∴ Average speed = $\frac{T o t a l D i s \tan c e}{T o t a l T i m e}$

$= \frac{(V T + 2.25 V T)}{(T + 1.5 T)}$

$ = \frac{3.25 V}{2.5} = 1.3 V$

∴ The average speed of the chartered bus for the entire journey is greater than its average speed in the morning by 30%.

Hence, option 2.

13. XAT 2012 QA | Arithmetic - Time, Speed & Distance

City Bus Corporation runs two buses from terminus A to terminus B, each bus making 5 round trips in a day. There are no stops in between. These buses ply back and forth on the same route at different but uniform speeds. Each morning the buses start at 7 AM from the respective terminuses. They meet for the first time at a distance of 7 km from terminus A. Their next meeting is at a distance of 4 km from terminus B, while travelling in opposite directions. Assuming that the time taken by the buses at the terminuses is negligibly small, and the cost of running a bus is Rs. 20 per km, find the daily cost of running the buses (in Rs.).

A.
3200
B.
4000
C.
6400
D.
6800
E.
None of the above

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

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