Time and Distance problems
- 1. A car runs at the speed of 50 km/h when not serviced and runs at 60 km/h, when serviced. After servicing, the car covers a certain distance in 6 h. How much time will the car take to cover the same distance when serviced?
Options- A. 8.2 h
- B. 6.5 h
- C. 8 h
- D. 7.2 h Discuss
Correct Answer: 7.2 h
Explanation:
After sevicing speed of car = 60 km/h
? Distance covered in 6 h = 60 x 6 km = 360 km.
When not serviced, then time taken to cover 360 km = 360/50 = 7.2 h
- 2. A and B are two station 1000 km apart. A train starts from A and moves towards B at 40 km/h. Another train starts from B at the same time and moves towards A at 60 km/h. How far from A will they cross each other?
Options- A. 350 km
- B. 400 km
- C. 525 km
- D. 300 km Discuss
Correct Answer: 400 km
Explanation:
Let they meet x km from A.
Then, according to the question,
x/40 = (1000 - x)/60
? 60 x = 40(1000 - x)
? 3x = 2000 - 2x
? 3x + 2x = 2000
? 5x = 2000 km
? x = 2000/5 = 400 km
- 3. A train runs for 3 h at the speed of 40 km/h and then for 4 1/ 2 h at the speed of 60 km/h. Thus, it covers 3/5th part of the whole distance. It wants to cover the remaining distance in 4 h, find the average speed of the train for remaining distance?
Options- A. 45 km/h
- B. 35 km/h
- C. 80 km/h
- D. 65 km/h Discuss
Correct Answer: 65 km/h
Explanation:
Let total distance = D
Now, according to the question,
40 x 3 + 60 x 4.5 = 3D/5
? 120 + 270 = 3D/5
? D = 390 x 5/3 = 650 km
? Remaining distance = [650 - (3/5) x 650]
= 650 - 390 = 260 km
Required average speed = 260/4 = 65 km/h
- 4. Two cars A and B start simultaneously from a certain place at the speed of 30 km/h and 45 km/h, respectively.The car B reaches the destination 2 h earlier than A. What is the distance between the starting point and destination?
Options- A. 90 km
- B. 180 km
- C. 270 km
- D. 360 km Discuss
Correct Answer: 180 km
Explanation:
Let the time taken by car B to reach destination is T h.
So, the time taken by car A to reach destination is (T + 2) h.
Now, S1T1 = S2T2
? 30(T + 2) = 45 x T
? 30T + 60 = 45T
? 15T = 60
? T = 4 h
Now, distance between starting point and destination = S2T2
= 45 x 4 = 180 km
- 5. Two ladies simultaneousely leave cities A and B connected by a strainght road and travel towards each other. The first lady travels 2km/h faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?
Options- A. 5 km,3 km
- B. 7 km, 5 km
- C. 8 km, 6 km
- D. 16 km, 14 km Discuss
Correct Answer: 8 km, 6 km
Explanation:
Let the speed of first lady be (v + 2)km/h and speed of second lady will be v km/h.
Total distance = 24 km
For first lady, Speed = Distance/Time
v + 2 = 24/t ...(i)
Let time taken by first lady to cover distance of 24 km be t h.
Then, time taken by second lady to cover same distance will be(t + 1)h.
For second lady, Speed =Distance/time
v = 24/(t + 1) ...(ii)
Form Eqs.(i) and (ii), we get
24/t - 2 = 24/(t + 1)
? (24 - 2t)/t = 24/(t + 1)
? (24 - 2t)(t + 1) = 24t
? 24t - 2t2 + 24 - 2t = 24t
? 2t2 + 2t - 24 = 0
? t2 + t - 12 = 0
? t2 + 4t - 3t - 12 = 0
? t(t + 4) -3(t + 4) = 0
? (t - 3)(t + 4) = 0
? t = 3, -4
? t = 3 (t ?- 4)
? The distance travelled by the first lady in one hour
= 24/t = 24/3 = 8 km
And distance travelled by the second lady in one hour
= 24/t + 1
= 24/3 + 1 = 6 km
- 6. The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?
Options- A. 456 kms
- B. 482 kms
- C. 552 kms
- D. 556 kms Discuss
Correct Answer: 552 kms
Explanation:
Total distance travelled in 12 hours =(35+37+39+.....upto 12 terms)
This is an A.P with first term, a=35, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 35+{12-1) x 2]
=6(70+23)
= 552 kms.
- 7. A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?
Options- A. 3.6
- B. 7.2
- C. 8.4
- D. 10 Discuss
Correct Answer: 7.2
Explanation:
Speed = = 2 m/sec = 2 x (18/5) km/hr = 7.2 km/hr
- 8. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
Options- A. 100 m
- B. 150 m
- C. 190 m
- D. 200 m Discuss
Correct Answer: 100 m
Explanation:
Relative speed of the thief and policeman = (11 ? 10) km/hr = 1 km/hr
Distance covered in 6 minutes = (1/60) x 6 km = 1/10 km = 100 m
Therefore, Distance between the thief and policeman = (200 ? 100) m = 100 m.
- 9. Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h
Options- A. 90 km/h
- B. 160 km/h
- C. 67.5 km/h
- D. None of these Discuss
Correct Answer: 160 km/h
Explanation:
- 10. Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, 5/6 hour before the second horse reaches A. If the distance between A and B is 50 km. what is the speed of the slower horse?
Options- A. 30 km/h
- B. 15 km/h
- C. 25 km/h
- D. 20 km/h Discuss
Correct Answer: 20 km/h
Explanation:
If the speed of the faster horse be and that of slower horse be then
and
Now, you can go through options.
The speed of slower horse is 20km/h
Since, 20+30=50
and
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