Latest Gate Aptitude Question SOLUTION: two cars start from the same point at the same time.the first car travells at constant speed of 12km/hr while second car travels at intial speed of 6km/hr,which increases by 1km/hr

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two cars start from the same point at the same time.the first car travells at constant speed of 12km/hr while second car travels at intial speed of 6km/hr,which increases by 1km/hr every hour.what will be the distance travelled by second car by the time it meets the first car

Asked In Gate potani manikumar (9 years ago)

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saikrishna  (8 years ago)

First car speed intervals per hour
12,12,12,12,12,..........n
So sum of the speed's can be written as 12*n...............EQUATION 1
Second car Speed intervals per hour
6,7,8,9,10,11,12...........n
So sum of the speeds would be
Sn=n/2[2a+{n-1}d]
Therefore sn=n/2[2*6+{n-1}1]
Simplifying sn=n/2[12+n-1]........................Equation 2
Equate equation 1 and 2 then we know where these equations would meet
12n=n/2[12+n-1]
Here do not cancel 12n with n/2 as we have to know the Value of n we shouldn't cancel it
so bringing 12n to the other side
n/2[12+n-1]-12n=0
sending the denominator 2 to the other side it becomes zero and 12n becomes 24n as it is multiplied by 2....
so the equation is n[12+n-1]-24n=0
12n+n^2-n-24n=0
n^2-13n=0
n^2=13n
n=13....
Here as we taken the sum of the speed's per hour and equated them to know when do they meet
now N mean after N hours those 2 equations meet so after 13hrs those two cars would meet
And now to know the distance travelled by 2nd car to meet 1st car after 13hrs
have to find the sum
6,7,8,.................18
sn=[first term+last term]/2 *n
6+18/2*13
24/2*13 therefore 12*13=156 is the ANSWER

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Priyanshu Agrawal  (9 years ago)

the distance travelled by second car will be 156km

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Somnath  (9 years ago)

156...Other than equations of motion..............
car a distance pattern---12,24,36,48........................seq..1
car B distance pattern--6,13,21,30,40.................. sequence 2
A/q car b meets A, so seq 2 will be at a term divisible by 12.......And following seq -2 the first number is 156..(Brute --force)

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potani manikumar  (9 years ago)

how,pls explain it

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parash  (9 years ago)

dist. travelled by 2nd car =144 km. ans
12*t=6t +1/2*1*t^2
(,12*t=ut+1/2(a*t)^2)
t(t-12)=0
t=12
total distance=12*12=144

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