Practice Questions for Arithmetic - Time, Speed & Distance

1. PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

A man can row 4.5 km/h in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of the stream.

(a)
1.5 kmph
(b)
2 kmph
(c)
2.5 kmph
(d)
1.75 kmph

2. PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

A car travels the first one-third of a certain distance with a speed of 10 km/h, the next one-third distance with a speed of 20 km/h, and the last one-third distance with a speed of 60 km/h. The average speed of the car for the whole journey is

(a)
18 kmph
(b)
24 kmph
(c)
30 kmph
(d)
36 kmph

Answer: Option A

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

Let the whole distance travelled be x km and the average speed of the car for the whole journey be y km/hr.

Then, $\frac{(x / 3)}{10} + \frac{(x / 3)}{20} + \frac{(x / 3)}{60} = \frac{x}{y}$

⇒ $\frac{x}{30} + \frac{x}{60} + \frac{x}{180} = \frac{x}{y}$

⇒ $\frac{1}{18} y$ = 1

⇒ y = 18 km/hr

Hence, option (a).

3. PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

Two runners run in the same direction along a circular track of 2 km long. The faster runner overtakes the slower one in every 30 minutes. Find their speeds if the faster one completes the track one minute sooner than the other.

(a)
24 km/h and 20 km/h
(b)
44 km/h and 28 km/h
(c)
20 km/h and 18 km/h
(d)
20 km/h and 16 km/h

Answer: Option A

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

Let x km/h and y km/h be the speeds of the two runners x > y

As per the question, $\frac{2}{y} - \frac{2}{x} = \frac{1}{60}$ …(1)

Also faster runner covers (x – y) km more than slower in 1 hr.

So, he will gain 2 km in $\frac{2}{(x - y)}$ hr or 1/2 hr. (30 min)

$\frac{2}{x - y} = \frac{1}{2}$ or, x – y = 4 …(2)

On solving (1) and (2), we get x = 24 km/h y = 20 km/h

Hence, option (a).

4. PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

Two trains are moving in opposite directions at speeds of 60 km/h and 90 km/h. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is

(a)
36
(b)
49
(c)
45
(d)
48

5. PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

A is twice as fast as B and B is thrice as fast as C is the journey covered by C in 1½ hours will be covered by A in

(a)
15 minutes
(b)
2 minutes
(c)
30 minutes
(d)
1 hour

6. PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

A motorcyclist covered two thirds of a total journey at his usual speed. He covered the remaining distance at three fourth of his usual speed. As a result, he arrived 30 minutes later than the time he would have taken at usual speed. If the total journey was 180 km, then what is his usual speed?

(a)
40 kmph
(b)
36 kmph
(c)
30 kmph
(d)
32 kmph

Answer: Option A

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

Total journey = 180 km

1/3^rd of journey = 180/3 = 60 km.

If usual speed be x km/h, then

$\frac{60}{\frac{3 x}{4}} - \frac{60}{x} = \frac{1}{2}$

⇒ $\frac{80}{x} - \frac{60}{x} = \frac{1}{2}$

⇒ $\frac{80 - 60}{x} = \frac{1}{2}$

⇒ x = 40 km/h

Hence, option (a).

7. PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

A man can row a certain distance against the stream in six hours. However, he would take two hours less to cover the same distance with the current. If the speed of the current is 2 km/h, then what is the rowing speed in still water?

(a)
10 kmph
(b)
12 kmph
(c)
14 kmph
(d)
8 kmph

Answer: Option A

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

If the rowing speed in still water be x km/h, and the distance by y km, then

$\frac{y}{x - 2} =$ 6

⇒ y = 6(x - 2) …(1)

and, $\frac{y}{x + 2}$ = 4

⇒ y = 4(x + 2) …(2)

⇒ 6(x - 2) = 4(x + 2)

⇒ x = 10 km/h

Hence, option (a).

8. PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

Two trains X and Y leave stations A and B, respectively, which are 180 km apart. Train X travels at a speed of 70 km/hr non-stop towards B. Train Y travels at 50 km/hr towards A, but stops for 15 min at a station known to be 50 km away from station B. At what approximate distance (in km) from station A will both the trains meet?

(a)
112
(b)
118
(c)
120
(d)
150
(e)
122

Answer: Option A

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

Total time taken by Y to cover 50 km = 50/50 = 1 hr.

It stops at station C for ¼ hr.

Now, in (1 + 1/4) hr, train X travels 70 × 5/4 = 87.5 km

This means they do not cross each other by the time train Y finishes its stop at station C.

Let them meet after t hr.

Then, 70t + 50 $(t - \frac{1}{4})$ = 180

⇒ t = 192.5/120 hr

Distance from A = $70 \times \frac{192.5}{120}$ km = 112 km (approximately).

Hence, option (a).

9. PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

If I walk at 4 km/h, I miss the bus by 10 minutes. If I walk at 5 km/h, I reach 5 minutes before the arrival of the bus. How far I walk to reach the bus stand?

(a)
5 kms
(b)
4.5 kms
(c)
5.25 kms
(d)
Cannot be determined

Answer: Option A

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

d = product of speed $[\frac{difference of time}{difference of speed}]$

d = $\frac{4 \times 5}{60} [\frac{10 - (- 5)}{5 - 4}]$ [Here, -ve sign indicates before the schedule time]

⇒ d = 5 km

Hence, option (a).

10. PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

Three men A, B and C walk around a circular path of length 1760 meters at the rate of 160, 120, 105 m/minutes respectively. If they start together and walk in the same direction, when will they first be together again?

(a)
5 hours 50 mins
(b)
5 hours 52 mins
(c)
6 hours 45 mins
(d)
None of these

PE 2 - Time, Speed & Distance | Arithmetic - Time, Speed & Distance

Feedback