Time and Distance problems
- 1. Starting from his house, one day a student walks at a speed of 3 km/h and reaches his school 5 min late. Next day he increases his speed by 1 km/h and reaches the school 3 min early. How far is the school from his house?
Options- A. 1.6 km
- B. 1.24 km
- C. 1.36 km
- D. 1.8 km Discuss
Correct Answer: 1.6 km
Explanation:
Let the distance be D km
Difference in timings = 8 min = 8/60 h = 2/15 h
? D/3 - D/4 = 2/15
? D/12 = 2/15
? D = 2 x 12/15 = 1.6 km
- 2. A thief running at 8 km/h is chased by a policeman whose speed is 10 km/h. If the thief is 100 m ahead of the policeman, then the time required for the policeman to catch the thief will be
Options- A. 2 min
- B. 3 min
- C. 4 min
- D. 6 min Discuss
Correct Answer: 3 min
Explanation:
Relative speed of policeman with thief = (10 - 8) = 2 km/h
Now, time taken to cover 100 m with speed of 2 km/h or 2000 m/h
Now, Speed = Distance / Time
? Time = D/S = 100/2000
= 1/20 h or 60/20 min = 3 min
- 3. A person can row 7 1/ 2 km/h in still water. It takes him twice as long to row up a distance as to row down the same distance. Find the speed of the stream?
Options- A. 2 km/h
- B. 2.2 km/h
- C. 2.5 km/h
- D. 2.7 km/h Discuss
Correct Answer: 2.5 km/h
Explanation:
Speed upstream + Speed downstream = 2 x 71/2 = 15 km/h
Since, the time taken is in the ratio 2 : 1
hence the speed will be in the ratio 1 : 2
? Speed upstream = (1/3) x 15 = 5 km/h
and speed downstream = (2/3) x 15 = 10 km/h
? Speed of stream = (10 - 5)/2 = 2.5 km/h
- 4. A streamer goes downstream from one port to another in 4 h. It covers the same distance upstream in 5 h. If the speed of the stream is 2 km/h , find the distance between the two ports?
Options- A. 50 km/h
- B. 60 km/h
- C. 70 km/h
- D. 80 km/h Discuss
Correct Answer: 80 km/h
Explanation:
Let the distance between the two ports = L km
Then, speed downstream = L/4
and speed upstream = L/5
? Speed of the stream = 1/2(L/4 - L/5)
? 1/2[(5L - 4L)/20] = 2
? L = 80 km
- 5. The current of a stream runs at 1 km/h. A motorboat goes 35 km upstream and back again at the starting point in 12 h. What is the speed of motorboat in still water?
Options- A. 7 km/h
- B. 4 km/h
- C. 6 km/h
- D. 5 km/h Discuss
Correct Answer: 6 km/h
Explanation:
Let the speed of boat in still water be V km/h. Then,
35/(V - 1) + 35/(V + 1) = 12
? 35(V + 1 + V - 1) = 12(V2 - 1)
? 6V2 - 35V - 6 = 0
? (V - 6)(6V + 1) = 0
? V = 6 (V = - 1/6 is not possible)
So, speed of boat in still water is 6 km/h.
- 6. The speed of a motorboat is 30 km/h. It starts from Mumbai at 6 am and reaches Goa at 8 am. Same day, it starts from Goa at 12 pm and reaches Mumbai at 4 pm. Find the the speed of stream.
Options- A. 8.5 km/h
- B. 12 km/h
- C. 10 km/h
- D. 11.5 km/h Discuss
Correct Answer: 10 km/h
Explanation:
Clearly, motorboat takes 2 h go from Mumbai to Goa and 4 h to go from Goa to Mumbai. i.e.,
Time taken to row upstream = 2 x Time taken to row downstream
? n = 2
Let the speed of stream be V km/h.
According to the formula,
Speed of boat = V(n + 1)/(n - 1)
? 30 = V(2 + 1)/(2 - 1)
? V = 30/3 = 10 km/h
- 7. At his usual rowing speed, Kapil can travel 12 miles downstream in a certain river in 6 h less than he takes to travel the same distance upstream. But, If he could double his usual rowing speed for his 24 miles round trip, the downstream 12 miles would then take only 1 h less than the upstream 12 miles. What is the speed of the current?
Options- A. 22/3 mile/h
- B. 32/3 mile/h
- C. 52/3 mile/h
- D. 72/3 mile/h Discuss
Correct Answer: 22/3 mile/h
Explanation:
Let speed of Kapil in still water = x
and speed of the current= y
? Speed upstream = (x - y)
and speed downstream = (x + y)
According to the question,
12/(x - y) - 12/(x + y) = 6
? 6(x2 - y2) = 24y
? x2 - y2 = 4y
? x2 = 4y + y2 ....(i)
Again, 12/(2x - y) - 12/(2x + y) = 1
? 4x2 - y2 = 24y
? x2 = (24y + y2)/4 ....(ii)
From Eqs. (i) and (ii), we get
4y + y2 = (24y + y2)/4
? 16y +4y2 = 24y + y2
? 3y2 = 8y
? y = 8/3 = 22/3 mile/h
- 8. A person riding a bike crosses a bridge with a speed of 54 km/h. What is the length of the bridge, if he takes 4 min to cross the bridge?
Options- A. 3600 m
- B. 2800 m
- C. 3500 m
- D. 4500 m Discuss
Correct Answer: 3600 m
Explanation:
Length of the bridge = Distance travelled by the person in 4 min = Speed x Time
Speed = 54 km/h = 54 x (5/18) = 3 x 5 = 15 m/s
Time = 4 min = 4 x 60 = 240 s
? Required length = 15 x 240 = 3600 m
- 9. Two men start together to walk a certain distance, one at 4 km/h and another at 3 km/h. The former arrives half an hour before the latter. Find the distance.
Options- A. 6 km
- B. 9 km
- C. 8 km
- D. 7 km Discuss
Correct Answer: 6 km
Explanation:
Let total distance = x km
According to the question,
x/3 - x/4 = 1/2;
? x/12 = 1/2
? x = 6 km
- 10. Aashutosh can cover a certain distance in 84 min by covering 2/3rd of distance at 4 km/h and the rest at 5 km/h. Find the total distance.
Options- A. 6 km
- B. 8 km
- C. 9 km
- D. 15 km Discuss
Correct Answer: 6 km
Explanation:
Let the total distance = L
Then, according to the question,
(2L/3)/ 4 + (1 - 2/3)L/5 = 84/60
? 2L/12 + L/15 = 84/60
? L/6 + L/15 = 84/60
? 5L + 2L = 42
? 7L = 42
? L = 42/7 = 6 km
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