Latest CTS Aptitude Question SOLUTION: Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25cm/s at what time they will collide with each other.

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Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25cm/s at what time they will collide with each other.

Asked In CTS Aparajita Chowdhury (12 years ago)

Solved subhendu bikash roy Read Solution (8)

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Read Solution (8) :

subhendu bikash roy  (12 years ago)

each car is moving forward for 100 cm with velocity 50cm/s
so time to cover 100cm is=100/50=2 sec
again receding back for 50 cm at 25cm/s velocity
so time to cover 50 cm is=50/25=2 sec
actually they individually cover (100-50)=50 cm in (2+2)=4 sec
so in 12 sec they together cover (150+150)=300 cm
and after that both move 100 cm in 2 sec
so after (12+2)=14 sec they cover (300+200)=500cm
so they collide after 14 sec

Is this solution Helpfull? Yes (29) | No (3)  

Vivek Gupta  (12 years ago)

total distance = 500cm
each car has to travel 250 cm to collide with each other

now, a car travels 100 cm forward with 50 cm/s speed => time taken = 2 secs
and 50 cm backward with a speed of 25 cm/s => tiime taken = 2 sec
so, for 4 secs each car travels 100 - 50 = 50 cms..
each car has to travel 250 cms to collide

from this point car will touch 150 cm in 6 sec (as after we got from above that car already travelled 50 cms) and then come back 50 cms in next two second

so actual distance travelled = 100 cms
actual time taken = 8 secs

in this way car again touch the 200 cm mile stone in next 2 secs and come back 50cm in next 4 secs
actual distance travelled in 12 secs is 150 cms

now actual distance is to travell 250 cms so remained is only 100 cms which the car will travell in next 2 secs and then collide

so the car will collide in 14 secs

so both cars collide after 20 secs.

Is this solution Helpfull? Yes (10) | No (8)  

snehasis karmakar  (12 years ago)

each is moving forward for 100cm at velocity 50cm/s and receding back for 50 cm at 25cm/s i.e in 4s every car covered 50cm
so every car has t covered 250cm path

So it takes (250/50)*4=20s when they meet

Is this solution Helpfull? Yes (2) | No (8)  

surya kamal  (7 years ago)

answer shuold be 14sec .previously submiited wrong answer

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Sushmidha Sakthiveeran  (7 years ago)

This is the "Frog in the Well" problem.

The question is: "How long does it take a car to move 250 cm forward?"


We can baby-step through the solution.

Draw a number line for reference.

. . begin{array}{cccccccccccc}
bullet & -- & bullet & -- & bullet & -- & bullet & -- & bullet & -- & bullet \
0 && 50 && 100 && 150 && 200 && 250 end{array}


In 2 seconds, it moves 100 cm forward.
In the next 2 seconds, it moves 50 cm back.
It is at "50".
. . In 4 seconds, it moved 50 cm forward.

In the next 4 seconds, it moves 50 cm forward.
. . It is at "100".

In the next 4 seconds, it moves 50 cm forward.
. . It is at "150".

In the next 2 seconds, it move 100 cm forward.
. . It is at "250".

Is this solution Helpfull? Yes (1) | No   

Aravinth Kumar  (7 years ago)

if both cars are moving forward separated by a distance moving at same rate, will they collide?

Is this solution Helpfull? Yes (1) | No (1)  

surya kamal  (7 years ago)

answer shold be 7sec

Is this solution Helpfull? Yes | No (2)  

parag  (7 years ago)

the ans is 20 secs
as each car covers 50 cm in 4 secs so in first 4 secs both moves towards each other i.e 50+50=100 cm in 4 sec.
so,500 cm in 4*5=20 secs

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