Time & Distance (12)

1. A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
1. 5
2. 6
3. 7
4. 8

Explanation :-

Speed of A = 2 rounds/hr    &    Speed of A = 2 rounds/hr
Relative speed = 2 + 3 = 5 rounds/hr
In 1 hour They cross each other = 5 times
In Half an hour They cross each other = 2 times
from 8 to 9:30 (1 and half hour ) they cross each other (5 + 2) = 7 times

2. Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
1. 17 hr
2. 14 hr
3. 12 hr
4. 19 hr

Explanation :-

Relative Speed  = 5.5 – 5 = 0.5 km/h
Distance = 8.5 km
Time = Distance/Speed
Time= 8.5 / 0.5 = 17 hrs

3. In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun’s speed?
1. 8 kmph
2. 5 kmph
3. 4 kmph
4. 7 kmph

Explanation :-

Let Arun’s speed = x km/h
(30/x) – 30/(2x) = 3
6x = 30     => x = 5 km/h

4. A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?
1. 12 km
2. 14 km
3. 16 km
4. 18 km

Explanation :-

Let’s assume distance covered on foot = x km.
Therefore , Distance covered on bicycle = (61 –x) km.
Time = Distance / Speed
(x/4) + (61 – x)/ 9 = 9
(9x + 244 -4x)/36 = 9
5x + 244 = 9*36
x = 16
Therefore, Distance traveled on foot = 4(4) = 16 km

5. Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?
1. 1 hr 42 min
2. 1 hr
3. 2 hr
4. 1 hr 12 min

Explanation :-

Let the original speed = x km/minute   &     time = t minutes
Distance (with original speed) = tx
Distance(with  speed slower speed) = (t+12) (6x/7)
As Both the distances are same
tx= (t+12) (6x/7)
t = 72 minuets (1 hr 12 min)

OR

Distance is directly related to speed,
Therefore at 6/7 the speed he will cover 7/6 the distance.
Therefore 1/6 the distance is covered in 12 min
2/6 the distance is covered in = 2*12 = 24 min

So, Whole Distance is covered in =  6 * 12 = 72 min