Time and Distance problems
- 1. A bullock cart has to cover a distance of 80 km in 10 h. If it covers half of the journey in 3/5th time, what should be its speed to cover the remaining distance in the left time?
Options- A. 5 km/h
- B. 10 km/h
- C. 15 km/h
- D. 18 km/h Discuss
Correct Answer: 10 km/h
Explanation:
Total distance to covered in 10 h = 80 km
But it covers 40 km in 3/5th of time, i.e, 40 km in 6 h.
? Required time = 10 - 6 = 4 h
And remaining distance = 40 km
Thus, required speed = 40/4 =10 km/h
- 2. Rani covers a certain distance by car driving at 5 km/h and returns the starting point riding on a scooter at 2 km/h. Find her average speed for the whole journey.
Options- A. 36/7 km/h
- B. 26/7 km/h
- C. 56/7 km/h
- D. 76/7 km/h Discuss
Correct Answer: 26/7 km/h
Explanation:
According to the formula,
Average speed = 2AB/(A + B)
Here, A = 5 km/h, and B = 2 km/h
? Required average speed = (2 x 5 x 2)/7 = 20/7
= 26/7 km/h
- 3. A person can walk a certain distance and drive back in 6 h. He can also walk both ways in 10 h. How much time will he take to drive both ways?
Options- A. 2 h
- B. 21/2 h
- C. 51/2 h
- D. 4 h Discuss
Correct Answer: 2 h
Explanation:
Given that, W + D = 6 ...(i)
[ w = Time taken while walking and
D = Time taken while driving ]
From Eq. (i)
5 +D = 6
? D = 1
2D = 2 x 1 = 2
? He will take 2 h to drive both ways.
- 4. Two men A and B travel from point P to Q, a distance of 84 km at 12 km/h and 16 km/h, respectively. B reaches Q and returns immediately and meet A at R. Find the distance form P to R.
Options- A. 72 km
- B. 76 km
- C. 78 km
- D. 68 km Discuss
Correct Answer: 72 km
Explanation:
Given, D = 84 km, a = 12 km/h and b = 16 km/ h
According to the formula
Distance traveled by A = PR = 2D x a/(a + b)
= 2 x 84 x 12/(12 + 16) = (2 x 84 x 12)/28
= 2 x 6 x 6 = 72 km
- 5. A thief is spotted by a policeman from a distance of 200 m. When the policeman starts chasing, the thief also starts running. If the speed of the thief be 16 km/h and that of the policeman be 20 km/h, how far the thief will have run before he is overtaken?
Options- A. 800 m
- B. 850 m
- C. 700 m
- D. 650 m Discuss
Correct Answer: 800 m
Explanation:
Relative speed of policeman = ( 20 - 16 ) x 5/18 = 10/9 m/s
To catch the thief, the policeman in has to gain 200 m = 200 x 9/10 = 180 s
Actual distance covered by policeman in 180 s = 180 x 50/9 = 100 m
? Distance covered by the thief = 1000 - 200 = 800m
- 6. A person sets out to cycle from A to B and at the same time another person starts from B to A. After passing each other, they complete their journeys in 16 h and 25 h, respectively. Find the ratio of speeds of the 1st man to that of the 2 nd man.
Options- A. 5 : 4
- B. 5 : 3
- C. 4 : 5
- D. 3 : 5 Discuss
Correct Answer: 5 : 4
Explanation:
Given, x = 16 and Y = 25
According to the formula,
1st man's speed : 2nd man's speed = ? y : ? x = ? 25 : ? 16 = 5 : 4
- 7. A certain distance is covered at a certain speed. If half of this distance is covered in 4 times of the time, then find the ratio of the two speeds.?
Options- A. 1 : 8
- B. 1 : 4
- C. 4 :1
- D. 8 : 1 Discuss
Correct Answer: 8 : 1
Explanation:
Let L km is covered in T h.
Then, first speed = L/T km/h
Again, L/2 km is covered in 4T h.
? New speed = (L/2 x 1/4T ) = (L/8T) km/ h
Ratio of speed = L/T : L/8T = 1 : 1/8 = 8 : 1
- 8. A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. Find his average speed.
Options- A. 3 km/h
- B. 4 km/h
- C. 4.5 km/h
- D. 9 km/h Discuss
Correct Answer: 4 km/h
Explanation:
Given, A = 6 km/h, B = 3 km/ h
According to the formula, Average speed = 2AB/(A + B)
? Required average speed = 2 x 6 x 3/(6 + 3)
= 36/9 = 4 km/h
- 9. A is twice as fast as B and B is thrice as fast as C. The journey covered by C in 56 min will be covered by A in?
Options- A. 51/3 min
- B. 21/3 min
- C. 71/3 min
- D. 91/3 min Discuss
Correct Answer: 91/3 min
Explanation:
Let time taken by A = Y
Let speed of C = x
Then, speed of B = 3x
? speed of A = 6x
Now, ratio of speeds of A and C = Ratio of time taken by C and A
6x : x = 56 : y
? 6x/x = 56/y
? y = 56/6 = 92/6
= 91/3 min
- 10. The ratio of the speeds of A and B is 3 : 4. A takes 20 min more than the time taken by B to reach a particular place. Find the time taken by A and B, respectively to reach that place.
Options- A. 40 min and 30 min
- B. 80 min 60 min
- C. 90 min and 45 min
- D. 90 min and 50 min Discuss
Correct Answer: 80 min 60 min
Explanation:
Ratio of speeds of A and B = 3 : 4
? Ratio of time taken = 4 : 3
Let time taken by A and B be 4k and 3k, respectively.
Then, according to the question,
4k - 3k = 20
? k = 20
Hence, time taken by A = 4 x 20 = 80 min
And time taken by B = 3 x 20 = 60 min
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