Time and distance

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11. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay’s speed is:
A. 5 kmph B. 6 kmph
C. 6.25 kmph D. 7.5 kmph

Answer: Option A

Explanation:

 

Let Abhay’s speed be x km/hr.

 

Then, 30 – 30 = 3
x 2x

6x = 30

x = 5 km/hr.
12. 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

Answer: Option C

Explanation:

 

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
13. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
A. 2 : 3 B. 3 : 2
C. 3 : 4 D. 4 : 3

Answer: Option C

Explanation:

 

Let the speed of the train be x km/hr and that of the car be y km/hr.

 

Then, 120 + 480 = 8       1 + 4 = 1 ….(i)
x y x y 15

 

And, 200 + 400 = 25     1 + 2 = 1 ….(ii)
x y 3 x y 24

Solving (i) and (ii), we get: x = 60 and y = 80.

Ratio of speeds = 60 : 80 = 3 : 4.
14. 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

Answer: Option C

Explanation:

 

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.
15. 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

Answer: Option D

Explanation:

 

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.

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