Latest CTS Aptitude Question SOLUTION: A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval. The car starts at 12 noon. Each bus tr

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(#M40002105) CTS Numerical Ability question Keep an EYE

A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval. The car starts at 12 noon. Each bus travels at a speed of 25 km/hr. Distance between A and B is 100 km. During its journey ,The number of buses that the car encounter is ?

Asked In CTS Aparajita Chowdhury (12 years ago)

Solved Aashu Read Solution (9)

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Read Solution (9) :

Rahul kumar singh  (12 years ago)

Betweem 6 am to 12pm ,12 buses are released from A (2*6=12 ,as per hour 2 buses are released).
Now the bus starting at 6am reaches B at 10am ,since time taken by bus to travel 100km is(100/25=4 hrs).Similarly,bus starting at 6.30am would reach B at 10.30am and so on..By the time it's 12pm the bus starting at 8am would have reached B.In this process a total of 5 buses had already arrived to B by 12pm.So,remaining(12-5),i.e,7 buses are on their way to B and will meet the car along the way.Now the car starting at 12pm takes(100/20=5 hrs) to reach A.Within this 5 hours (5*2) i.e.,10 more buses are released which will also meet Car on it's way.So ,we have(7+10)=17 buses meeting car on it's way.
:-)

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Aashu  (12 years ago)

Total journey = 100 km.
The bus travel starts from A at a time of 6 A.M. and each bus travels at a speed of 25 km/hr so time required for the bus to complete the journey = 4 hrs.
so the bus starts at 8:30 will meet with the car moving in opposite direction definitely.
Car travels from B at a speed of 20 km/hr so time of arrival of car at A is 5 P.M., it means the last bus which will meet with the car is that starts at 4:30 P.M.
so total bus ranges from 8:30 P.M. to 4:30 P.M. = 17

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AJAY CHAUDHARY  (12 years ago)

ans- 5 buses
EXPLANATION-
first we have to find time to cover distance 100km by bus & it will be 100/24=4 hrs.
it means first bus will reach point B at 10am
second....................................10:30
3..........................................11:00
4..........................................11:30
5...........................................12:00pm
5th bus will also encounter the bus because of greater speed.....

Is this solution Helpfull? Yes (3) | No (15)  

prabhu  (12 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.

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".


Therefore, they will collide in 14 seconds.

Is this solution Helpfull? Yes (1) | No (12)  

Dante  (12 years ago)

As we need to know the counter of the bus and car..we should take with respective to the car..The car makes one journey only but bus can make many journeys.
so From 12pm to 5 pm they meet for every 30 min..Ans=>11

Is this solution Helpfull? Yes (1) | No (5)  

priya  (12 years ago)

19 buses. when car starts at 12:00 it comes accross the bus of 8:00, From this moment until it reaches to its destination at 17:00 (including the 17:00 bus), there are 19 buses around.

Is this solution Helpfull? Yes (1) | No (5)  

niranjan  (8 years ago)

Betweem 6 am to 12pm ,12 buses are released from A (2*6=12 ,as per hour 2 buses are released).
Now the bus starting at 6am reaches B at 10am ,since time taken by bus to travel 100km is(100/25=4 hrs).Similarly,bus starting at 6.30am would reach B at 10.30am and so on..By the time it's 12pm the bus starting at 8am would have reached B.In this process a total of 5 buses had already arrived to B by 12pm.So,remaining(12-5),i.e,7 buses are on their way to B and will meet the car along the way.Now the car starting at 12pm takes(100/20=5 hrs) to reach A.Within this 5 hours (5*2) i.e.,10 more buses are released which will also meet Car on it's way.So ,we have(7+10)=17 buses meeting car on it's way

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shweta poddar  (12 years ago)

it shud be 11

Is this solution Helpfull? Yes | No (7)  

bikram nayak  (9 years ago)

ans shud be 15

Is this solution Helpfull? Yes | No (5)  

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