Sample questions for time and distance problems

Hyderabad: 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

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/4 km 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

Banda Ravipal Reddy

Director, SIGMA

Sai Institute of General Mental Ability

Hyderabad