Latest TCS Aptitude Question SOLUTION: Two cars start from the same point at the same time towards the same destination which is 420 km away. The first and second car travel at respective speeds of 60 kmph and 90 kmph.

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Two cars start from the same point at the same time towards the same destination which is 420 km away. The first and second car travel at respective speeds of 60 kmph and 90 kmph. After travelling for sometime the speed s of the two cars get interchanged. Finally the second car reaches the destination one hour earlier than the first. Find the time after which the speeds get interchanged?

Asked In TCS dipali (10 years ago)

Unsolved Read Solution (19)

Is this Puzzle helpful?   (28)   (14) Submit Your Solution Time Distance and Speed

Read Solution (19) :

Karthika  (10 years ago)

Try it this way..
car A at 60 kmph :___60___|___120___|__180___|__240___|__300___|__360__|__420__|
car B at 90 kmph :___90___|___180___|__270___|__360___|__450___|

Our destination is only 420km.
So now the interchanging speeds such that car B reaches 1 hour less than car A,

Car A now at 90kmph aftr 240km: ___60___|___120___|__180___|__240___|__(240+90=330)___|__(330+90=20)__|

Car B now at 60kmph after 360km: ___90___|___180___|__270___|__360___|__(360+60=420)___|

So from figure car B reaches one hour less than car A.
So from the figure car B reaches

Is this solution Helpfull? Yes (38) | No (2)  

sambasiva rao  (10 years ago)

first A & B travels x hours
after exchange A travels y+1 hours and B travels y hours
A speed 60
B speed 90
60x+90(y+1)=420 eq--->1
90x+60y=420 eq--->2
by solving eq---> 1&2
60x+90(y+1)=90x+60y
30x-30y=90
form this x=4,y=1
the speeds are exchanged after 4 hours...

Is this solution Helpfull? Yes (33) | No   

GEEVEE  (10 years ago)

let the speed be interchanged after 'k' hrs
A B
distance covered in 'k' hrs(km) 60k 90k
remaining distance(km) 420-60k 420-90k
new speed(kmph) 90 60
time to cover remaining distance (420-60k)/90--->slow (420-90k)/60---->fast

slow - fast = 1
(420-60k)/90 - (420-90k)/60 = 1
on solving we get
25k-70=30
25k=100
k=4----->(ans)

Is this solution Helpfull? Yes (18) | No   

PRIYADHARSHINI  (10 years ago)

hi rudra....for 1st 4 hrs A covers 240km and B covers 360km...if their speeds get interchanged after this A still need 2hrs to cover remaining(180 km) and B needs 1hr to cover remaining distance(60km)...therefore B covers 1hr earlier than A...

Is this solution Helpfull? Yes (9) | No   

sujeet kumar keshri  (10 years ago)

let after travelling X km they interchange their speeds.
Ta=(X/60) + (420-X)/90 ...........1
Tb=(X/90) + (420-X)/60 ...........2
a/c Ta=Tb+1 ......................3
after solving we get X=50 km
time at which they inter change their speeds = X/60 = 50/60 = 5/6 hrs

Is this solution Helpfull? Yes (6) | No (7)  

Amit Gupta  (10 years ago)

near about 2 hours

Is this solution Helpfull? Yes (3) | No (5)  

Nitin  (10 years ago)

Why this Kolaveri D?

Time taken by Ist car = 420/60=7hrs
Now let after T hours the speeds get interchanged.
So for Ist car:
Distance traveled in T hours with 60KPH + Distance traveled in (6-T)hours with 90 KPH speed = 420
60T+90(6-T)=420
Solve it for T. You will get T=4hours
Note : I have taken 6-T because the total time(7) was reduced by 1Hr.

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

PRIYADHARSHINI  (10 years ago)

speed gets interchahged after the end of 4th hour...

Is this solution Helpfull? Yes (1) | No (2)  

Karthika  (10 years ago)

Edit*
Try it this way..
car A at 60 kmph :___60___|___120___|__180___|__240___|__300___|__360__|__420__|
car B at 90 kmph :___90___|___180___|__270___|__360___|__450___|

Our destination is only 420km.
So now interchanging speeds such that car B reaches 1 hour less than car A,

Car A now at 90kmph aftr 240km: ___60___|___120___|__180___|__240___|__(240+90=330)___|__(330+90=20)__|

Car B now at 60kmph after 360km: ___90___|___180___|__270___|__360___|__(360+60=420)___|

So from figure car B reaches one hour less than car A.

Is this solution Helpfull? Yes (1) | No   

Brajeshrai  (8 years ago)

let speed get interchanged after X hr.
(420-60x)/90=(420-90x)/60)+1
after solving we get x=4

Is this solution Helpfull? Yes (1) | No   

Rupesh Kumar  (8 years ago)

Let the total time taken by the cars be a and b
Let the time after which the speed is interchanged be t
For car A, 60t+90(a-t) = 420, 90a - 30t = 420 .......(1)
For car B, 90t + 60(b-t) = 420, 60b + 30t = 420 ....(2)
Using both (1) and (2), we get 90a + 60b = 840
But as a - b =1, 90a + 60(a-1) = 840.
Solving a = 6.
Substituting in equation 1, we get t = 4

Is this solution Helpfull? Yes (1) | No   

Devendra Marghade  (10 years ago)

If measured by distance then, after travelling 300 Km, the speed of the cars was interchanged.
Anybody have an idea about the time ? pl. explain

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mohit rai  (10 years ago)

after 4 hours speeds get interchanged

Is this solution Helpfull? Yes | No (1)  

Rudra  (10 years ago)

@priyadharshini plzzz explain in detail

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Rudra  (10 years ago)

@priyadharshini Hi...I got it.....thank u very much

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ayushi garg  (10 years ago)

can anyone plz explain it to me wid full solution

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rishu diwan  (9 years ago)

Let the total time taken by the cars be a and b
Let the time after which the speed is interchanged be t
For car A, 60t+90(a-t) = 420, 90a - 30t = 420 .......(1)
For car B, 90t + 60(b-t) = 420, 60b + 30t = 420 ....(2)
Using both (1) and (2), we get 90a + 60b = 840
But as a - b =1, 90a + 60(a-1) = 840.
Solving a = 6.
Substituting in equation 1, we get t = 4

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Mohd Shoeb  (8 years ago)

After 4 hours..

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ajay das  (8 years ago)

Let the total time taken by the cars be a and b Let the time after which the speed is interchanged be t For car A, 60t+90(a-t) = 420, 90a - 30t = 420 .......(1) For car B, 90t + 60(b-t) = 420, 60b + 30t = 420 ....(2) Using both (1) and (2), we get 90a + 60b = 840 But as a - b =1, 90a + 60(a-1) = 840. Solving a = 6. Substituting in equation 1, we get t = 4

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