Time, Speed & Distance - Previous Year IPM/BBA Questions
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Here we bring you all previous year Time, Speed & Distance IPMAT - Indore questions along with detailed solutions.
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Vinita drives a car which has four gears. The speed of the car in the fourth gear is five times its speed in the first gear. The car takes twice the time to travel a certain distance in the second gear as compared to the third gear. In a 100 km journey, if Vinita travels equal distances in each of the gears, she takes 585 minutes to complete the journey. Instead, if the distances covered in the first, second, third, and fourth gears are 4 km, 4 km, 32 km, and 60 km, respectively, then the total time taken, in minutes, to complete the journey, will be______.
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Answer:312
Text Explanation :
The speed of the car in the fourth gear is five times its speed in the first gear
⇒ Let the speed in 1st gear be x kmph, hence speed in 4th gear will be 5x kmph.
The car takes twice the time to travel a certain distance in the second gear as compared to the third gear
⇒ Speed in 3rd gear is twice the speed in 2nd gear.
⇒ Let speeds in 2nd and 3rd gears be y & 2y kmph.
In a 100 km journey, if Vinita travels equal distances in each of the gears, she takes 585 minutes
⇒ 25/x + 25/5x + 25/y + 25/2y = 585/60
⇒ 25/x + 5/x + 50/2y + 25/2y = 39/4
⇒ 30/x + 75/2y = 39/4
⇒ 60/x + 75/y = 39/2
⇒ 20/x + 25/y = 13/2
⇒ 5(4/x + 5/y) = 13/2
⇒ 4/x + 5/y = 13/10 ...(1)
Now, we need to find the time taken if Vinita travels 4, 4, 32, 60 kms at 1st, 2nd, 3rd & 4th gear respectively.
⇒ 4/x + 4/y + 32/2y + 60/5x
= 4/x + 4/y + 16/y + 12/x
= 16/x + 20/y
= 4(4/x + 5/y)
= 4 × 13/10
= 5.2 hours
= 5.2 × 60 minutes
= 312 minutes
A helicopter flies along the sides of a square field of side length 100 kms. The first side is covered at a speed of 100 kms, and for each subsequent side the speed is increased by 100 kmph till it covers all the sides. The average speed of the helicopter is
When Geeta increases her speed from 12km/hr to 20km/hr, she takes one hour less than the usual time to cover the distance between her home and office. The distance between her home and office is ___________ km.
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Answer:30
Text Explanation :
Let the times taken at 12 kmph is t hours, hence the time taken at 20 kmph is (t - 1) hours.
In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?
(a)
80
(b)
100
(c)
150
(d)
50
Answer: Option
A
Text Explanation :
In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?
Ashok beat Bipin by 150 metres or 15 seconds.
∴ Speed of Bipin = 150/15 = 10 m/s
Bipin takes = 400/10 = 40 seconds to complete the race.
Time taken by Ashok to complete the race = 40 - 15 = 25 seconds
Time taken by Chandan to complete the race = 25 + 25 = 50 seconds
Distance travelled by Chandan in 40 seconds = 400/50 × 40 = 320 metres.
∴ By the time (40 secs) Bipin completes the race, Chandan has completed 320 m and hence Bipin beats Chandan by 80 meters.
A train left point A at 12 noon. Two hours later, another train started from point A in the same direction. It overtook the first train at 8 PM. It is known that the sum of the speeds of the two trains is 140 km/hr. Then, at what time would the second train overtake the first train, if instead the second train had started from point A in the same direction 5 hours after the first train? Assume that both the trains travel at constant speeds.
(a)
3 am the next day
(b)
4 am the next day
(c)
8 am the next day
(d)
11 pm the same day
Answer: Option
C
Text Explanation :
Case 1: Train 2 starts 2 hours after Train 1.
Train 1 travels from 12 pm till 8 pm i.e., for 8 hours.
Same distance is travelled by Train 2 from 2 pm till 8 pm i.e., in 6 hours.
∴ Ratio of speeds of Train 1 and Train 2 = 6 : 8 = 3 : 4
⇒ Let speed of Train 1 = 3x and Train 2 = 4x
⇒ 3x + 4x = 140
⇒ x = 20
⇒ Speed of Train 1 = 60 kmph, Speed of Train 2 = 80 kmph.
Case 2: Train 2 starts 5 hours after Train 1.
Train 1 would have travelled 5 × 60 = 300 kms when Train 2 starts i.e., at 5 pm.
Relative speed of the two trains = 80 - 60 = 20 kmph.
∴ Time for Train 2 after it starts to meet Train 1 = 300/20 = 15 hours.
Two friends run a 3-kilometer race along a circular course of length 300 meters. If their speeds are in the ratio 3:2, the number of times the winner passes the other is __________.
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Answer:3
Text Explanation :
Since the ratio of their speeds is 3 : 2, they will meet at only one point on the circular track and that point will be the starting point.
Hence, when they meet for the first time, the faster person travels 3 rounds, the slower person would travel 2 rounds.
i.e., when the faster person travels 3 × 300 = 900 meters, they meet once.
∴ When the faster person travels 2700 (3 × 900) meters, they would have met 3 times.
To meet for the 4th time faster person needs to travel 900 meters more, but he has only 300 meters of the race left.
∴ Now the faster person would complete the race before they meet for the 4th time.
Two small insects, which are x metres apart, take u minutes to pass each other when they are flying towards each other, and v minutes to meet each other when they are flying in the same direction. Then, the ratio of the speed of the slower insect to that of the faster insect is
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