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:

by
[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:

by
[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.

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.

by
[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

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:

by
[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.

5

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.?

by
[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.

10

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

Required speed =

60
kmph.
= 12 kmph.

5