Time & Distance topic is some of the most important quantitative aptitude topics asked in the exams. The questions involving time, and distance are to be solved using the distance formulas and concepts that you can refer to solve the questions.
Problems and Solutions
Q1: Walking 3/4th of his usual speed, a person is 10 min late to his office. Find his usual time to cover the distance?
Solution:Usual time = Late time/old time – new time
Usual time = 10/4/3 -1
Usual time = 10/1/3
Usual time = 30 min
Q2: Running 4/3rd of his usual speed, a person improves his timing by 10 min. Find his usual time to cover the distance?
Solution:New time – Old time = Early
x-3/4x = 10 min
x = 40 min
Q3: A man covers a certain distance between his house and office on scooter having an average speed of 30 km/hr; he is late by 10 min. However, with as speed of 40 km/hr, he reaches his office 5 min earlier. Find the distance between his house and office?
Solution:Let the distance be x km
Difference between time taken = 15 min = 1/4 hr
x/30 – x/40 = 1/4
x = 30 km
Q4: Two trains for Patna leave Delhi at 10am and 10:30 am and travel at 600000 km/hr and 75 km/hr respectively. How many kilometers from Delhi will the two trains be together?
Solution:Meeting point distance = Product of 2 speeds/Difference of 2 speeds * difference in time
= (60*75/75-60) *30/60
= 150 km
Q5: An aero plane covers a certain distance at a speed of 240 km/hr in 1 2/3 hrs , it must travel at a speed of _____?
Solution:Distance = Speed * Time
Distance = 240 * 5
Distance = 1200km
NewTime = 1 2/3 hr
NewTime = 5/3 hr
Hence new speed = 1200/5/3
new speed = 240*3
new speed = 720 km/hr
Q6: Two men A and B walk from P to Q, a distance of 21 km at 4 km/hr respectively. B reaches q, returns immediately and meets A at R. Find the distance from p to R?
Solution:Distance travelled by A = 2 * distance of 2 points (a/a+b)
Distance travelled by B = 2 * distance of 2 points (b/a+b )
Then, distance travelled by A= 2*21*3/7 = 18 km.
Q7: A train travelling 25 km/hr leaves Delhi at 9am and another train travelling 35 km/hr starts at 2 pm in the same direction. How many kilometers from Delhi will them together?
Solution:Meeting point distance from starting point
S1 * S2 * difference in time/difference in speed
25*35*5/10
437.5 km.
Q8: The distance b/w two stations, Delhi and Amritsar is 450 km. a train starts at 4 pm from Delhi and moves towards Amritsar at on average speed of 60 km/hr. Amritsar train starts from Amritsar at 3:20 pm and moves towards Delhi at an average speed of 80km/hr. How far from Delhi will be the two trains meet and at what time?
Solution:Let distance be x km
(Time taken by B to cover (450-x) km) – Time taken by A cover x km = 40/60
450-x/80 = x/60
x = 40/60
Time taken by A to cover 170 km = 170/60 hrs
= 2 hrs 50 min
So the train meets at 6:50 pm.
Q9: If a person walks at 14 km/hr instead of 10 km/hr. He would have walked 20 km more. What is the actual distance travelled by him?
Solution:let the distance be x km
x/10 = x+20/14
x = 50 km
Q10: If a train with a speed of 60 km/hr cross a pole in 30sec. Find the length of a train?
Solution:Distance = Speed * Time
Distance = (60*5/18)*30
Distance = 500meters
Q11: A 100m long train with a speed of 30km/hr can cross a man in how much time?
Solution:100 = 30 * 5/18 * T
T = 12sec
Q12: A Train can cross 2 men going along the railways track at 4 km/hr and 5 km/hr in same direction in 10 sec and 12 sec. Find the length of the train?
Solution:(x-4) * 5/18 * 10 = (x-5) * 5/18 * 12
5x-20 = 6x-30
x = 10km/hr
Length of train = (10-40)*5/18*10
Length of train = 50/3meters
Q13: A Train pass two person who are walking in opposite in direction, the train is moving at 5m/sec and 10m/sec in 6sec and 5sec respectively. Find the length of the Train?
Solution:(x+5)*6 = (x+10)*5
x = 20m/sec
Length of train = (20+5)*6
Length of train = 150 meters
Q14: Two trains starts at same time from Delhi and Jaipur towards each other with a sped of 80 km/hr and 95 km/hr. When they meet faster train cover 180 km more distance than the other. Find the distance b/w Delhi and Jaipur?
Solution:Let they meet after x hr
So distance travelled by first train in x hrs = 80x
Distance travelled by second train in x hrs = 95x
Distance between Delhi and jaipur = 80x+95x = 175x
Now 95x-80x = 180km
15x = 180
x = 12hr
So they will meet after 12 hrs
Distance between Delhi and jaipur = 175*12 = 2100km
Q15: A person running at 7/11 of its usual speed reached a place in 22 hrs. How much time would he save had he run his normal speed?
Solution:Distance = 7/11s*22
Distance = 14s --------> 1
Let t be the time taken by the train to reach the place with its actual speed
Distance = Speed * time --------> 2
From 1 and 2, we get
14s = s*t
t = 14hrs
Time that could be saved = 22-14 = 8hrs.
Q16: A train leaves Patna at 5 am and reaches Delhi at 9 am. Another train leaves Delhi at 6:30 am and reaches Patna at 10 am. At what time do the two trains meet?
Solution:They will meet = 5am + (9-5)*(10-5)/(9-5) + (10-6:30)
They will meet = 5am + 4*5/7.5
They will meet = 5 + 2 * 2/3
They will meet = 7:40am
Q17: When a man travels equals distance at speeds v1 and v2 km/hr, his average speed is 4km/hr. But when he travels at these speeds for equal time's average speed is 4.5 km/hr. Find the difference in two speeds?
Solution:v1-v2 = sqrt(product of average speeds * Difference of average speeds)
v1-v2 = sqrt(4*4.5*0.5)
v1-v2 = sqrt(9)
v1-v2 = 3km/hr
Q18: Two trains start at the same time from Hyderabad and Delhi and proceed towards each other at the root of 80 and 95 km/hr. When they meet, it is found that, one train has travelled 180km more than other. Find the distance between Delhi and Hyderabad?
Solution:Relative speed = 80+95 = 175km/hr
Faster train travels 15kms more = 180/15 = 12hrs
Distance = 175 * 12 = 2100km
Q19: A man takes 8hrs to walk to a certain place and ride back. However, he could have gained 2hrs. If he had covered both ways by riding. How long he take to walk both ways?
Solution:W * R = 8
2 * R = 6
R = 3
W = 5 then both ways W+W = 10hrs
Q20: A man ride a certain distance by train at the rate of 25km/hr and walked back at the rate of 4km/hr. Whole journey took 5hrs 48minutes. What distance did he ride?
Solution:Distance = Total time * Product of 2 speeds/sum of 2 speeds
Distance = (24/5) * (25*4/29)
Distance = 20km
K. Mahesh
Aptitude Trainer