Time and Distance problems
- 1. A person covers half of his journey at 40 km/h, one-third at 60 km/h and rest of journey at 30 km/h. Find his average speed for the whole journey.?
Options- A. 45 km/h
- B. 42. 35 km/h
- C. 50 km/h
- D. 40 km/h Discuss
Correct Answer: 42. 35 km/h
Explanation:
Let total distance be 100 km.
Then, Average = 100/[ (50/40) + (30/60) + (20/30)]
= 100/( 5/4 + 1/2 + 2/3) = 100/[(15 + 6 + 8)/12]
= (100 x 12)/29
= 42.35
- 2. Mohan walking at a speed of 20 km/h reaches his office 1 h late. Next time he increases his speed by 5 km/h, then he reaches his office 30 min early. What is the distance of his office from his house?
Options- A. 100 km
- B. 125 km
- C. 150 km
- D. None of the above Discuss
Correct Answer: 150 km
Explanation:
Distance of his office from his house = {ab/(b - a)} x (t1 + t2)
Here, a = 20 km/h, t1 = 1 h, b = 20 + 5 = 25 km/h
and t2 = 30 min = 0.5 h
? Distance = {20 x 25/(25 - 20)} x (1 + 0.5) = 500(1.5)/5
= 100 x 1.5 = 150 km
- 3. A boy walking at a speed of 15 km/h reaches his school 20 min late. Next time he increases his speed by 5 km/h but still he late by 5 min. Find the distance of the school from his home.?
Options- A. 5 km
- B. 10 km
- C. 15 km
- D. 20 km Discuss
Correct Answer: 15 km
Explanation:
Let the distance = x
Here, the difference in time
= 20 - 5 = 15 min
= 15/60 = 1/4h
Speed during next journey
= 15 + 5 = 20 km/h
According to the question,
x/15 - x/20 = 1/4
? 4x - 3x/60 = 1/4
? x = 60/4 = 15
? x = 15 km
- 4. For every 4 leaps taken by a dog, a cat takes 5 leaps in the same time. But distance covered in 3 leaps of dog is same as that of 4 leaps of cat. Then what is the ratio of speed of dog and cat?
Options- A. 15 : 14
- B. 16 :15
- C. 12 :11
- D. 10 : 9 Discuss
Correct Answer: 16 :15
Explanation:
Let distance covered by dog in 1 leap is x and
Distance covered by cat in 1 leap is y
Then, 3x = 4y
? x= 4/3y
Now, Ratio of speed of dog and cat = Ratio of distance covered by them in the same time = 4x : 5y
= 16/3y : 5y
= 16 : 15
- 5. Suresh traveled 1200 km by air which formed (2/5) of his trip. One-third of the whole trip he traveled by car And the rest of the journey he performed by train. The distance traveled by train was?
Options- A. 1600 km.
- B. 800 km.
- C. 1800 km.
- D. 400 km. Discuss
Correct Answer: 800 km.
Explanation:
Let the total distance be y km.
Then, 2y / 5 = 1200
? y = (1200 x 5) /2 = 3000 km.
Distance traveled by car
= (1/3 X 3000) = 1000 km.
Distance traveled by train
= [3000- (1200 + 1000) ] km.
= 800 km.
- 6. Two cyclists A and B start from the same place at the same time. One going toward north at 18 km/hr. and other going toward south at 20 km/hr. What time will they take to be 95 km. apart?
Options- A. 4 hrs. 30 min.
- B. 4 hrs. 45 min.
- C. 5 hrs.16 min.
- D. 2hrs. 30 min Discuss
Correct Answer: 2hrs. 30 min
Explanation:
Relative velocity = u + v = 18 + 20 = 38 km
They are 38 km. apart in 1 hr.
? They will be 95 km. apart in ( 95 / 38) hrs.
= 2 hrs . 30 min
- 7. A bullock cart has to cover a distance of 80 km. in 10 hours. If it cover half of journey in 3/5 th time, what should be its speed to cover the remaining distance in time left?
Options- A. 8 km/hr.
- B. 20 km/hr.
- C. 6.4 km/hr.
- D. 10 km/hr. Discuss
Correct Answer: 10 km/hr.
Explanation:
Distance left = (1/2 x 80 ) km. = 40km.
Time left - [(1-3/5) x 10 ] hrs.
= 4 hours
Required speed = (40 / 4 ) km/hr
= 10 km/hr.
- 8. The ratio between the rates of travelling of A and B is 2:3 and therefore A takes 10 min. more than the time taken by B to reach a destination, if A had walked at double the speed, he would have covered the distance in?
Options- A. 30 min
- B. 25 min
- C. 15 min
- D. 20 Min Discuss
Correct Answer: 15 min
Explanation:
Ratio of times taken by A and B = 1/2 : 1/3
Suppose B takes Tb min. Then A takes (Tb + 10) min.
? (Tb + 10 ) : Tb = 1/2: 1/3
? (Tb + 10)/Tb = 3 / 2
? 2Tb + 20 = 3Tb
? Tb = 20
? Time taken by A = 20 +10
= 30 minute
If A had walked at double speed
Req . time = 30/2
=15 minute
- 9. A man travel 35 km partly at 4 km/hr if he covers former distance at 5 km/hr and later distance at 4 km/hr he could cover 2 km. more in the same time. The time taken to cover the whole distance at original rate is?
Options- A. 9 hours
- B. 7 hours
- C. 4 1/2 hours
- D. 8 hours Discuss
Correct Answer: 8 hours
Explanation:
Suppose the man covers first distance in x hrs and second distance in y hrs.
Then, 4x + 5y = 35 and 5x + 4y = 37
Solving these equations, we get
x = 5 and y = 3
? Total time taken = 5 + 3 hrs.
= 8 hrs.
- 10. If a train run at 40 km/hr it reaches its destination late by 11 min but if it run at 50 km/hr it is late by 5 min only. The correct time for the train to cover at journey is?
Options- A. 13 min.
- B. 15 min.
- C. 21 min.
- D. 19 min. Discuss
Correct Answer: 19 min.
Explanation:
Let the required time = T min.
Then, distance covered in T + 11 min at 40 km/hr = distance covered in T + 5 min at 50 km/hr.
? 40 ( T + 11 ) / 60 = 50 (T + 5 ) / 60
? T = 19 min.
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