Sample questions for time and distance problems (tslprb)
This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and solutions on the Time and Distance topic.
1. The ratio between the speeds of two trains is 7:8. If the second train runs 400 kms in 4 hours, then the speed of the first train is?
Solution:
Let the Speed of 1st train = 7x and
2nd train = 8x
8x = 400/4
x = 12.5
7x = 7 × 12.5
= 87.5 km/hr
2. A man travelled from the village to the post-office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the
distance of the post-office from the village?
Solution:
Average Speed =
2xy/(x + y)= (2 ×25 ×4)/(25 + 4) = 200/29 km/hr
Time = 5 hours 48 min =
5 × 48/60 hrs = 5 × 4/5 hrs
= 29/5 hrs
Total Distance =
29/5 × 200/29 = 40 km
The distance between village and post office = 40/2 = 20 km
3. Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time anywhere on the track if they are moving in opposite directions?
Solution:
Relative Speed = 15 + 25
= 40 km/hr = 40 × 5/18
= 100/9 km/hr
D = 300 m
Time taken to meet for the first time anywhere on the track = 300 × 9/100
= 27 seconds
4. A man covers half of his journey by train at 60 km/hr, half of the remaining by bus at 30 km/hr and the rest by cycle at 10 km/hr. Find his average speed during the entire journey.
Solution:
Let the total Distance = x km
First part of the Distance
D1 = x/2 km
Time T1 = x/(2 ×60)
= x/120 hrs
Second part of the Distance D2 = x/4km Time T2 = x/(4 ×30) = x/120 hrs
Remaining Distance D3 = x/4 km Time T3 = x/(4 ×10)
= x/40 hrs
Average Speed = (Total Distance)/(Total Time) = x/(x/120 + x/120 + x/40) = x/((x +x +3x)/120)
=x × 120/5x = 24 km/hr
5. A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is:
Solution:
Time taken to walk both ways = 7 hours 45 minutes ——(1)
Time taken to walking one way and riding back
= 6 hours 15 minutes
——(2)
2(Time taken to walking one way and riding back)
= 12 hours 30 minutes
——(3)
By equation (3) – (1)
=>, we have
Time taken to man ride both ways
= 12 hours 30 minutes – 7 hours 45 minutes
= 4 hours 45 minutes
6. With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 35 km/hr, it is late by 15 minutes. Find the length of the total journey.
Solution:
Let Time = x hrs
So 40x = 35(x +15/60)
40x = 35x + 35/4
5x = 35/4
x = 7/4 hrs
Therefore, total length of the journey = 7/4 × 40 = 70 km
