- Manav drives from his home to the nearest metro station at an average apeed of 40km. From station, he boards a train that takes him to his office at a speed of 80km. the entire distance covered by him is 52km and the entire journey took him 1 hour. find the distance between the station from where he boards the train and his office.
Explanation: let from his home to station distance = x
(x/40) + ((52-x)/80) = 1
solving this x = 28 km
so from office to station = 52-x = 52-28 = 24 km
2. Two trains for B leave A at 6.30am and 7.40am and travel at 30km/hr and 40 km./he respectively. How many kms from A will the trains meet?
Explanation: suppose they will meet after x hr.
30x=40(x-7/6) (Time gap between train A and B is 1hr 10min=7/6hr)
By solving x=14/3
they will meet at distance=30*14/3=140km
3. In a kilometre race, if A gives B a 40 m start, A wins by 19 s But if A gives B a 30 s start, B wins by 40 m.Find the time taken by B to run 5,000 m?
Explanation: Analyzing the 2 cases,Case1: when A travels 1Km,B travels 960 – 19 x where B’s speed=x m/s
Case 2:when A travels 960 m,B travels 1000-30 x
In both cases,time remains constant.therefor,Distance is directly proportional to speed.
1000/(960-19x) = 960/(1000-30x)
solving x,we get x=20/3 m/s.Time taken to travel 5000 m for B is 12.5 hr.
4. straight line between 2 places is 3000m. A person moves with 6/11km/hr from p to q @12pm and another person moves from opposite direction with speed 5/22km/hr from q to p @ 1pm.when they will meet together?
Explanation: the person from p moves 6/11 km in 1 hr so 3-6/11=27/11
6/11 t+5/22 t=27/11
so time=4:17 pm
5. Hemant and Ajay start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lane and at uniform speed, but Hemant is faster than Ajay.They first pass at a point 18.5 m from the deep end and having completed one length, each one is allowed to rest on the edge for exactly 45 seconds.After setting off on the return length, the swimmers pass for the second time just 10.5 m from the shallow end.How long is the pool?
Explanation: let the speed is a & b (b>a)
total distance =x
two equation will form
18.5/a=(x-18.5)/b (Deep end equation)
x/b+45+10.5/b=x/a+45+(x-10.5)/a (swallow end equation)
equating 1 & 2
we get a/b=37/53
6. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
Explanation: If the length of fast train=x, then
time taken to cross a man sitting in slower train=time taken to cross the distance equal to length of the faster train with the relative speed of 40-20=20 km/hr.
So x/20=5/3600, x=1/36 Km. or 1000/36 m=27.77 meters.
7. A 270 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.
Explanation: train running in the opposite than total speed=(80+120)=200 kmph
let lenght of another train is l meterthan
8. How many seconds will a 500 meter long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
Explanation: train and man ismoving in the same direction so the relative speed will be= (633)km/hr= 60km/hr
then 60km/hr * 5/18= 50/3 m/sec
therefore, time = distance/speed
= 500/ (50/3)
= 30 seconds
so the answer is 30 seconds
9. Ratio between speeds of 2 trains is 5:3. If the first train runs 350 km in 2 hours, then what is the speed of the second train?
Explanation: (speed of train 1 / speed of train 2 ) = 5/3
(175 / S2 ) = 5/3
- A car is 250 metres behind the bus. The car and bus are moving with speed 60 km/hr and 35km/hr respectively. The car will be ahead of bus by 250 metres in:
A: 37 seconds
B: 48 seconds
C: 72 seconds
D: 68 seconds
Correct Answer : C
Explanation: Relative speed=60-35=25 Km/hr
For car to be ahead of bus by 250 meter,distance to be covered=250+250=500m=0.5km
So time taken=0.5/25=1/50 Hr or 3600/50=72 seconds
- Mohan walks a certain distance and rides back in 6 hours and 15 minutes. If he walks both ways he takes 7 hours and 45 minutes. If Mohan rides both ways the time which he will take will be:
A: 4 hours
B: 4hours 45min
C: 9/2 hours
D: 17/4 hours
Correct Answer : B
Explanation :Time taken in walking both the ways = 7 hours 45 minutes ——– (i)
Time taken in walking one way and riding back = 6 hours 15 minutes ———– (ii)
By the equation (ii)*2 – (i), we have,
Time taken by the man in riding both ways,
= 12 hours 30 minutes – 7 hours 45 minutes
= 4 hours 45 minutes.
- A train leaves Delhi at 6.00 a.m. and reaches Agra at 10.00 a.m. Another train leaves Agra at 8.00a.m. and reaches Delhi at 11.30 a.m. At what time do the two trains cross each other if the distance between Delhi and Agra is 200 km?
A: 8.45 a.m.
B: 8.56 a.m.
C: 9.20 a.m.
D: 9.56 a.m.
Correct Answer : B
Explanation: Speed of first=s=200/4=50km/h
Speed of second=S=200/3.5=400/7km/h
Till 8 A.M. first one has already covered 50 x 2=100 Kms
So now both are 100 km apart
They are approaching each other
So relative speed=50+400/7=750/7 Km/h
Time=100/(750/7)=700/750=14/15 hours=14×60/15=56 minutes
So they will cross each other at 8.56A.M
- A ship is moving at a speed of 30 kmph. To know the depth of the ocean beneath it, it sends a radiowave which travels at a speed 200 m/s. The ship receives back the signal after it has moved 500 m. What is the depth of the ocean?
A: 4 km
B: 8 km
C: 6 km
D: 12 km
Correct Answer : C
Explanation: dist. traveled by radiowaves = 2d=speed X time
=> 2d = 200 X 60
=> d = 100X60=6000m
so the depth of the ocean is 6 km or 6000m
- Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
A. 906 km
B. 960 m
C. 960 km
D. 966 km
Explanation: Answer: Option C
60(x + 1) = 64x
X = 15
60 * 16 = 960 km
- If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
A. /5 km
B. 5/4 km
C. 6/5 km
D. 3/4 km
Answer: Option A
x/3 – x/4 = 4/60
x = 4/5 km
- Walking 6/7th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is:
A. 11 hr 4242 min
B. 11 hr
C. 22 hr
D. 11 hr 1212 min
Answer: Option D
New speed =6/7=6/7 of usual speed
Speed and time are inversely proportional.
Hence new time =7/6=7/6 of usual time
Hence, 7/67/6 of usual time – usual time =12=12 minutes
⇒1/6⇒1/6 of usual time =12=12 minutes
Therefore, usual time =12×6=72=12×6=72 minutes
=1=1 hour 1212 minutes
17. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
A. 2 : 1
B. 3 : 2
C. 8 : 3
D. Cannot be determined
None of these
Let the man’s rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs. Let the man’s rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
18. A boat covers a certain distance downstream in 1 hour, while it comes back in 11/2 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
A. 12 kmph
B. 13 kmph
C. 14 kmph
D. 15 kmph
E. None of these
Explanation: Let the speed of the boat in still water be x kmph. Then,
Speed downstream = (x + 3) kmph,
Speed upstream = (x – 3) kmph.
∴ (x + 3) x 1 = (x – 3) x 3/2
⇒ 2x + 6 = 3x – 9
⇒ x = 15 kmph
19. Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
Answer: Option C
RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m = 175 m
20. How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Answer: Option C
D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps = 250/10 = 25 sec