DXC Quants Problems on Trains Quiz 1

Answer: C
Explanation:
Let the distance between A and B be x
The second car starts 3 hours later and reaches 5 hours early then first car
so the time difference is 8 hours.
Thus, x/20 - x/ 30 = 8
or, x = 480 km

Answer: C
Explanation:
Let the speed of the Autorikshaw be x and y respectively
length of Autorikshaw 1 = 81x
length of Autorikshaw 2 = 51y
Since, Both trains running in opposite directions
Relative speed= x + y
Time taken to cross each other = 69 seconds
=> (81x + 51y)/(x + y) = 69
=> (81x + 51y) = 69(x + y)
=> 12x = 18y
=> x/y = 18/12 = 3/2

Answer: B
Explanation:
According to the formula, Time = Distance/ Speed
Thus, Time = 500/ 90 x 5/18 (multiplying by 5/18 to change km/h into m/s)
or, Time = 20 sec.

Answer: B

Explanation:

The Speed of the Bus starting from Motihari = 200/4 = 50 km/h

The Speed of the Bus starting from Muzaffarpur = 200/5 = 40 km/h

Suppose the two Buses meet x hours after 6.00 am

Then x * 50 + (x - 2) * 40 = 200

or, 50x + 40x - 80 = 200

or, 90x = 280 

or, x = 280/90 ~ 3.1 hrs

Hence, the required time = 9:06 a.m

Answer: B

Explanation:

Let its slower speed = V km per hour

Here distance is same in both the cases

Using the formula = V1 x t1 = V2 x t2 

or, V x 10 = (V + 6) x 7

or, 10 V = (V + 6) x 7 

3V = 42

V = 14

Thus, the Slower speed of the Bus is 14 km/h.

Answer: B
Explanation:
Let the length of the second lorry be X.
Speed of both the lorry = (66 - 30) x 5/18 = 10 m/s
Thus, (150 + X)/5 = 90 sec
or, 150 + X = 450
or, X = 300 m

Answer: B
Explanation:
Since both firetruck are moving in opposite directions
Relative speed = x + y.
Total distance covered = 200 +200 = 400 m
Time = 20 s
let speed of the slower firetruck is v . Then the speed of the faster firetruck is 2v
(Since one is moving twice as fast the other)
Relative speed = v + 2v = 3v
3v = 400/20 m/s = 20 m/s
=> v = 20/3 m/s
Speed of the faster firetruck= 2v = 40/3 m/s = (40/3)×(18/5) km/hr = 8 x 6 = 48 km/hr

Answer: B
Explanation:
Let the distance be x between the two stations.
Train A takes 5 hours to reach Jharkhand.
Train B takes 6 hours to reach Patna.
The relative speed of both the train will be added = x/5 + x/ 6 = 11x/30
Time taken = x/11x/30 = 30/11
or, (30 X 60 )/11 =~ 2:43 hours
so 8 + 2.43 = 10:43 am

Answer: C
Explanation:
First bus travels 30 min at speed of 80 kmph
distance = 80 x 1/2 = 40 km
Then bus travels 45 min at a speed of 120 kmph
distance = 120 x 3/4 = 90 km,
at last, it travels 2 hours at speed of 150 kmph
distance = 150 x 2 = 300 km

Total distance = 40 + 90 + 300 = 430 km
Total time= 1/2 + 3/4 + 2 = 3.25 hr
Average speed of the bus= 430/3.25 = 132.30 km/h

Answer : Option c
Explanation :
Assume both trains meet after x hours after 9 a.m.
Distance covered by train starting from M in x hours = 20x km
Distance covered by train starting from N in (x-1) hours = 50(x-1)
Total distance = 220
=> 20x + 50(x-1) = 110
=> 70x = 160
=> x= 160/70 ~ 2.3 hrs
This means, they meet after 2 hours and 18 mins after 9 a.m., ie, they meet at 11:18 a.m.