Time and Distance

1. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:

[A]. 14 km

[B]. 15 km

[C]. 16 km

[D]. 17 km

✅ The correct answer is option C.
Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.

So,
x
+
(61 -x)
= 9

4
9

9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km.

2. A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:

[A]. 35

[B]. 36 2 3

[C]. 37 1 2

[D]. 40

✅ The correct answer is option D.
Let distance = x km and usual rate = y kmph.

Then,
x
–
x
=
40
2y(y + 3) = 9x ….(i)

y
y + 3
60

And,
x
–
x
=
40
y(y – 2) = 3x ….(ii)

y -2
y
60

On dividing (i) by (ii), we get: x = 40.

3. A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

[A]. 3.6

[B]. 7.2

[C]. 8.4

[D]. 10

✅ The correct answer is option B.
Speed =

600
m/sec.

5 x 60

= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)

2 x
18

km/hr

= 7.2 km/hr.

4. A car travelling with of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.

[A]. 17 6 km/hr 7

[B]. 25 km/hr

[C]. 30 km/hr

[D]. 35 km/hr

✅ The correct answer is option D.
Time taken = 1 hr 40 min 48 sec = 1 hr 40
4
min = 1
51
hrs =
126
hrs.

5
75
75

Let the actual speed be x km/hr.

Then,
5
x x
126
= 42

7
75

x =

42 x 7 x 75

= 35 km/hr.

5 x 126

5. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:

[A]. 50 km

[B]. 56 km

[C]. 70 km

[D]. 80 km

✅ The correct answer is option A.
Let the actual distance travelled be x km.

Then,
x
=
x + 20

10
14

14x = 10x + 200
4x = 200
x = 50 km.

6. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

[A]. 9

[B]. 10

[C]. 12

[D]. 20

✅ The correct answer is option B.
Due to stoppages, it covers 9 km less.

Time taken to cover 9 km =

9
x 60
min
= 10 min.

7. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

[A]. 100 kmph

[B]. 110 kmph

[C]. 120 kmph

[D]. 130 kmph

✅ The correct answer is option C.
Let speed of the car be x kmph.

Then, speed of the train =
150
x
=

3
x
kmph.

100
2

75
–
75
=
125

x
(3/2)x
10 x 60

75
–
50
=
5

x
x
24

x =

25 x24

= 120 kmph.

8. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

[A]. 70 km/hr

[B]. 75 km/hr

[C]. 84 km/hr

[D]. 87.5 km/hr

✅ The correct answer is option D.
Let the speed of two trains be 7x and 8x km/hr.

Then, 8x =

400

= 100

x =

100

= 12.5

Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

9. A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

[A]. 220 km

[B]. 224 km

[C]. 230 km

[D]. 234 km

✅ The correct answer is option B.
(1/2)x
+
(1/2)x
= 10

21
24

x
+
x
= 20

21
24

15x = 168 x 20

x =

168 x 20

= 224 km.

10. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

[A]. 8 kmph

[B]. 11 kmph

[C]. 12 kmph

[D]. 14 kmph

✅ The correct answer is option C.
Let the distance travelled by x km.

Then,
x
–
x
= 2

10
15

3x – 2x = 60
x = 60 km.

Time taken to travel 60 km at 10 km/hr =

60
hrs
= 6 hrs.

So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.

Required speed =

60
kmph.
= 12 kmph.