## Slot -2 – Quantitative Aptitude – Arithmetic – Time Speed and Distance – Points A, P, Q and B lie on the same line

Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets car 1 at Q, and car 2 at P. If each car is moving in uniform speed then the ratio of the speed of car 2 to that of car 1 is?

a) 2 : 7

b) 2 : 9

c) 1 : 4

d) 1 : 2

Solution:
Car 2 and car 3 meets at Q, so ratio of their speed = AQ : BQ = 200 : 100 = 2:1

Car 1 and car 3 meets at P, so ratio of their speed = AP : BP = 100 : 200 = 1 : 2

So required ratio of speed of car 1 and car 2 = 1 : 4

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## Slot -2 – Quantitative Aptitude – Arithmetic – Time Speed and Distance – On a long stretch of east-west road

On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs. The diﬀerence between their speeds, in km per hour, is?

Solution:

Let the speeds of Cars are v and u . then, v+u=350———–1)
and v-u=350/7=50———-2)

So required difference in speeds=50 km/hr

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## Slot -2 – Quantitative Aptitude – Arithmetic – Time Speed and Distance – Points A and B are 150 km apart

Points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A. Each car travels at a speed of 100 kmph for the ﬁrst 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km. The distance, in km, between car 2 and B when car 1 reaches B is (TITA )?

Solution:
Time taken by Car 1 to travel first 20 km =20/100 hr =1/5 hr

Thus Car 2 will reach B 12 minutes after Car 1 will reach.

Thus Required distance = time×speed=1/5×25=5 km

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## Slot -1 – Quantitative Aptitude – Arithmetic – Time Speed and Distance – Point P lies between points A and B

Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is?

Solution:

Ratio of time taken by car 1 and car 2 = (x/2v) : (3x/v) = 1 : 6 = t : 6t

Given 6t – t = 60 minutes

Or 5t = 60

Thus t = 12 minutes

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## Slot -1 – Quantitative Aptitude – Arithmetic – Time Speed and Distance – The distance from A to B is 60 km

The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is?

a) 5

b) 3

c) 4

d) 6

Solution: let time taken by Narayan to reach B = t hour

So time taken by Partha to reach B = (t+4) hours

Time taken by Partha to reach mid point of A and B = (t+ 4)/2

Given t – (t+ 4)/2 = 2

2t – t – 4 = 4

t = 8 hours

Speed of Partha = 60/(t+4) = 60/12 = 5 km/hour

Correct option a) 5

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## Slot -1 – Quantitative Aptitude – Arithmetic – Time Speed and Distance – Train T leaves station X for station Y

Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance between X and Z is three-ﬁfths of that between X and Y. How many hours does train T take for its journey from X to Y? (TITA)

Solution:
Let the total distance XY = 5x so XZ = 3x and YZ = 2x
Ratio of time taken by train T and train S to reach Z from their respective Station = (3x/v : 2x/3v/4)
= 9 : 8
Thus ( 9t -1 ) = 8t
t = 1
so time taken by train T to cover 3x = 9 hour
so time taken by train T to cover XY ( 5x ) = 5/3 *9 = 15 hour

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