Quantitative Aptitude DI
Sep 10 2020
Here we are providing new series of Quantitative Aptitude Questions for upcoming exams, so the aspirants can practice it on a daily basis.
Directions (1 - 5): Study the following information carefully and answer the given questions?
The following table shows the sum of length of five trains, ie, A, B, C, D and E, and the time taken by those two trains completely crossing each other when they are both running in opposite directions.
1) Find the time taken by train A to cross train D, if they travel in same direction?
a) 44 sec
b) 52 sec
c) 56 sec
d) 60 sec
e) None of these
2) In the question, two quantities I and II are given. You have to solve both the quantities to establish the correct relation between Quantity I and Quantity II and choose the correct option.
Quantity I:Train B crossed a tunnel in 27.5 seconds, if another train P of length same as tunnel and the speed of train P is 90 km/hr crossed train B when both the trains are travelling in the same direction, then find the time taken by the train P to cross train B?
Quantity II: Find the time taken by Train E crosses a man standing in the platform of length 300 m?
a) Quantity I = Quantity II
b) Quantity I< Quantity II
c) Quantity I ≤ Quantity II
d) Quantity I> Quantity II
e) Quantity I ≥ Quantity II
3) The length of which of the following trains is less than the average length of all the five trains?
a) Train A and Train B
b) Train C and Train E
c) Train A and Train C
d) Both b and c
e) Can’t be determined
4) In the question, three quantities I, II and III are given. You have to solve all the given quantities to establish the correct relation between QuantityI, II and III and choose the correct option.
Quantity I: Find the sum of time taken by train B crosses train D while travelling on opposite directions and the time taken by train C crosses train E while travelling on opposite directions?
Quantity II: Find the time taken by train A to cross train C while travelling on same directions?
Quantity III: Find the time taken by train B to cross a tunnel of length 120 m?
a) Quantity I > Quantity II > Quantity III
b) Quantity I = Quantity II > Quantity III
c) Quantity I > Quantity II < Quantity III
d) Quantity I = Quantity II < Quantity III
e) Quantity I ≥ Quantity II ≤ Quantity III
5) When travelling in the same direction a car can cross the train D in 8 seconds. If the speed of the car is more than that of train, then find the total distance travelled by the car in 5 hours?
a) 750 km
b) 900 km
c) 640 km
d) Cannot be determined
e) None of these
Answers:
Directions (1 – 5):
Let the speed of train A, B, C, D and E be a, b, c, d and e m/s respectively and the length of train A, B, C, D and E be p, q, r, s and t metres respectively.
The lengths,
p + q = 500, q + r = 450, r + s = 390, s + t = 420, t + p = 380
Then,
2 * (p + q + r + s + t) = 500 + 450 + 390 + 420 + 380
p + q + r + s + t = 2140 / 2 = 1070
The length of train A = 1070 – (450 + 420) = 200 m
The length of train B = 1070 – (390 + 380) = 300 m
The length of train C = 1070 – (500 + 420) = 150 m
The length of train D = 390 - 150 = 240 m
The length of train E = 1070 – (500 + 390) = 180 m
Now, when trains cross each other moving in opposite directions,
a + b = 500 / 10 = 50
b + c = 450 / 15 = 30
c + d = 390 / 13 = 30
d + e = 420 / 8.4= 50
e + a = 380 / (19 / 3) = 60
Then,
2 * (a + b + c + d + e) = 50 + 30 + 30 + 50 + 60
a + b + c + d + e = 220 / 2 = 110
The speed of train A = 110 – (30 + 50) = 30 m/s
The speed of train B = 110 – (60 + 30) = 20 m/s
The speed of train C = 110 – (50 + 50) = 10 m/s
The speed of train D = 110 – (60 + 30) = 20 m/s
The speed of train E = 110 – (50 + 30) = 30 m/s
1) Answer: C
Required time = (200 + 240) / ((30 – 20)
= > 440 / 10 = 44 sec
2) Answer: D
Quantity I:
The length of train B = 300 m
The speed of train B = 20 m/s
According to the question,
(300 + TL) / 20 = 27.5
300+ TL = 550
TL = 250
The length of tunnel = 250 m = The length of train P
The speed of train B = 90 * (5/18) = 25 m/s
The time taken by the train P to cross train B
= > (300 + 250) / (25 - 20)
= > 110 sec
Quantity II:
The time taken by Train E crosses a man standing in the platform,
We doesn’t take the platform length. They mention that, the man is standing in the platform only. So, we take the man length., ie, 0.
= > 180 / 30
= > 6 sec
Quantity I> Quantity II
3) Answer: D
The sum of length of all the five trains
2 * (p + q + r + s + t) = 500 + 450 + 390 + 420 + 380
p + q + r + s + t = 2140 / 2 = 1070
The average length of all the five trains
= > (1070 / 5) = 214 m
Train A, C and E have less length than the average length.
So, the required answer is, Both b and c
4) Answer: C
Quantity I:
Time taken by train B crosses train D while travelling on opposite directions
= > (300 + 240) / (20 + 20)
= > 540 / 40 = 13.5 sec
Time taken by train C crosses train E while travelling on opposite directions
= > (150 + 180) / (10 + 30)
= > 330 / 40 = 8.25 sec
Required sum = 13.5 + 8.25 = 21.75 sec
Quantity II:
Time taken by train A to cross train C while travelling on same directions
= > (200 + 150) / (30 - 10)
=> 350 / 20 = 17.5 sec
Quantity III:
Time taken by train B to cross a tunnel of length 120 m
= > (300 + 120) / 20
= > 420 / 20 = 21 sec
Quantity I > Quantity II < Quantity III
5) Answer: B
Let the speed of car be x m/s,
According to the question,
= > 240 / (x - 20) = 8
= > x - 20 = 30
= > x = 50
The speed of car = 50 m/s = 50 * (18/5) = 180 km/hr
The total distance travelled by the car in 5 hours
= > 180 * 5 = 900 km