Time and Distance problems
- 1. P, Q and R start simultaneously from A to B. P reaches B, turns back and meet Q at a distance of 11 km from B. Q reached B, turns back and meet R at a distance of 9 km from B. If the ratio of the speeds of P and R is 3:2, what is the distance between A and B ?
Options- A. 99
- B. 100
- C. 89
- D. 1 Also asked in: AIEEE, Bank PO, Bank Clerk, Analyst, GATE, CAT, Bank Exams
Correct Answer: 99
Explanation:
Let, Distance between A and B = d
Distance travelled by P while it meets Q = d + 11
Distance travelled by Q while it meets P = d ? 11
Distance travelled by Q while it meets R = d + 9
Distance travelled by R while it meets Q = d ? 9
Here the ratio of speeds of P & Q => SP : SQ = d + 11 : d ? 11
The ratio of speeds of Q & R => SQ : SR = d + 9 : d ? 9
But given Ratio of speeds of P & R => P : R = 3 : 2
=> = 3/2
=> d = 1, 99
=> d = 99 satisfies.
Therefore, Distance between A and B = 99
- 2. Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
Options- A. 15 hours
- B. 16 hours
- C. 17 hours
- D. 18 hours Also asked in: GRE
Correct Answer: 17 hours
Explanation:
In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph ? 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs
- 3. A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles
Options- A. 60bm/c
- B. bm/60c
- C. bc/60m
- D. 60b/cm Also asked in: GRE
Correct Answer: bm/60c
Explanation:
Substitute sensible numbers and work out the problem. Then change the numbers back to letters. For example if the machine puts 6 caps on bottles in 2 minutes, it will put 6 /2 caps on per minute, or (6 /2) x 60 caps per hour. Putting letters back this is 60c/m.If you divide the required number of caps (b) by the caps per hour you will get time taken in hours. This gives bm/60c
- 4. A son and father goes for boating in river upstream . After rowing for 1 mile son notices the hat of his father falling in the river. After 5 min he tells his father that his hat has fallen. So they turn round and are able to pick the hat at the point from where they began boating after 5min. Find the speed of river in miles/hours ?
Options- A. 4 mile/hr
- B. 6 mile/hr
- C. 2 mile/hr
- D. 5 mile/hr Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk
Correct Answer: 6 mile/hr
Explanation:
Let the speed of river and boat be 'r' m/min and 'b' m/min.
so relative speed in upstream (b-r)m/min and in downstream (b+r)m/min.
Now in upstream distnce covered in 5 min is 5(b-r)miles
so total distnce covered => 1 + 5(b-r)miles in upstream
In downstream distance covered in 5min is 5(b+r)miles
Now 1 + 5(b-r) = 5(b+r)
1+5b-5r = 5b+5r
1 = 10r
r = 1/10 mile/min => 6 mile/hr.
- 5. Ashwin fires two bullets from the same place at an interval of 15 minutes but Rahul sitting in a bus approaching the place hears the second sound 14 minutes 30 seconds after the first. If sound travels at the speed of 330 meter per second, what is the approximate speed of bus?
Options- A. 330/29 m/s
- B. 330 x 30 m/s
- C. 330/14 m/s
- D. 330/900 m/s Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 330/29 m/s
Explanation:
Second gun shot take 30 sec to reach rahul imples distance between two.
given speed of sound = 330 m/s
Now, distance = 330 m/s x 30 sec
Hence, speed of the bus = d/t = 330x30/(14x60 + 30) = 330/29 m/s.
- 6. If a girl cycles at 10 kmph, then she arrives at a certain place at 1 p.m. If she cycles at 15 kmph, she will arrive at the same place at 11 a.m. At what speed must she cycle to get there at noon?
Options- A. 14 kmph
- B. 13 kmph
- C. 12 kmph
- D. 11 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 12 kmph
Explanation:
The distance is constant in this case.
Let the time taken for travel with a speed of 10 kmph be 't'.
Now the speed of 15 kmph is 3/2 times the speed of 10 kmph.
Therefore, time taken with the speed of 15 kmph will be 2t/3 (speed is inversely proportional to time)
Extra time taken = t - 2t/3 = t/3
=> 1pm - 11am = 2hrs
=> t/3 = 2h
=> t = 6 hrs.
Now, Distance = speed x time = 10 x 6 = 60 kms
Time he takes to reach at noon = 6 - 1 = 5 hrs
Now, Speed = 60/5 = 12 kmph.
- 7. A man covers a distance of 1200 km in 70 days resting 9 hours a day, if he rests 10 hours a day and walks with speed 1½ times of the previous in how many days will he cover 840 km ?
Options- A. 39 days
- B. 37 days
- C. 35 days
- D. 33 days Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 35 days
Explanation:
Distance d = 1200km
let S be the speed
he walks 15 hours a day(i.e 24 - 9)
so totally he walks for 70 x 15 = 1050hrs.
S = 1200/1050 => 120/105 = 24/21 => 8/7kmph
given 1 1/2 of previous speed
so 3/2 * 8/7= 24/14 = 12/7
New speed = 12/7kmph
Now he rests 10 hrs a day that means he walks 14 hrs a day.
time = 840 x 7 /12 => 490 hrs
=> 490/14 = 35 days
So he will take 35 days to cover 840 km.
- 8. Chennai express left Hyderabad for Chennai at 14 : 30 hours, travelling at a speed of 60 kmph and Charminar Express left Hyderabad for Chennai on the same day at 16 : 30 hours, travelling at a speed of 80 kmph. How far away from Hyderabad will the two trains meet?
Options- A. 360 kms
- B. 480 kms
- C. 520 kms
- D. 240 kms Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 480 kms
Explanation:
Now, the distance covered by Chennai express in 2 hrs = 60 x 2 = 120 kms
Let the Charminar Express takes 't' hrs to catch Chennai express
=> 80 x t = 60 x (2 + t)
=> 80 t = 120 + 60t
=> t = 6 hrs
Therefore, the distance away from Hyderabad the two trains meet = 80 x 6 = 480 kms.
- 9. Three friends Rudra, Siva and Anvesh start to run around a circular stadium. They complete a revolution in 24, 36 and 30 seconds respectively. After how many minutes will they meet at the starting point ?
Options- A. 60
- B. 120
- C. 360
- D. 6 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 6
Explanation:
For this we have to find the LCM of 24, 36 and 30
LCM of 24, 36 and 30 = 360 sec
360/60 min = 6 minutes.
- 10. A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed ?
Options- A. 1hr
- B. 1 hr 20 min
- C. 1 hr 10 min
- D. 50 min Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 1 hr 20 min
Explanation:
Let the distance and original speed be 'd' km and 'k' kmph respectively.
d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3
=> (5d - 4d)/4k = 1/3 => d = 4/3 k
Time taken to cover the distance at original speed
= d/k = 4/3 hours = 1 hour 20 minutes.
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