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abhishekdadarwal2009
Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 5


Sol speed
A 30
B 40
K 60

Inorder for all of them reach at the same time at the same point. we have to take the LCM

which is 120.

for this distance the time taken by A ,B and K will be 4,3,2 but this does not fit in the questions.

so we take the next point where they may meet which is 240.

the time taken by A,B and K is 7,6 and 4 respectivly.
from this we get hat ther is a difference of 3 hours. Sol A.

Shouldn't it take A 8 hours to travel 240 KM if he's going 30 KM/Hour? So the times would be A=8 B=6 K=4. This lines up if you double the KM from 120 to 240, because then the times will double along with it (4,3,2 ---> 8,6,4)

Therefore the answer is 4 (Sol C)
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abhishekdadarwal2009
Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 5


Sol speed
A 30
B 40
K 60

Inorder for all of them reach at the same time at the same point. we have to take the LCM

which is 120.

for this distance the time taken by A ,B and K will be 4,3,2 but this does not fit in the questions.

so we take the next point where they may meet which is 240.

the time taken by A,B and K is 7 ,6 and 4 respectivly. It should be 8,6,4 So the difference is 4 not 3
from this we get hat ther is a difference of 3 hours. Sol A.

Dear abhishekdadarwal2009 ,

I have highlighted your mistake, Please check.
IMO-C
Regards!!
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rajatchopra1994
abhishekdadarwal2009
Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 5


Sol speed
A 30
B 40
K 60

Inorder for all of them reach at the same time at the same point. we have to take the LCM

which is 120.

for this distance the time taken by A ,B and K will be 4,3,2 but this does not fit in the questions.

so we take the next point where they may meet which is 240.

the time taken by A,B and K is 7 ,6 and 4 respectivly. It should be 8,6,4 So the difference is 4 not 3
from this we get hat ther is a difference of 3 hours. Sol A.

Dear abhishekdadarwal2009 ,

I have highlighted your mistake, Please check.
IMO-C
Regards!!


Agreed and corrected!! well i guess i should be careful while writing the solutions. Cheers!
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Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 5


Please som help here!!!!

What am I doing wrong? My logic was the following:

Suppose A started at 00:00. (In two hrs we would have travelled 60 kms)

B started at 2:00 am and has to complete 60kms with a speed of 10kmph (40kmph - 30kmph = 10kmph).

60kms/10kmphr = 6hrs

So B will overtake A after 6 hrs, so at 8:00 am. (He started at 2:00am, 2 hrs after A who started at 00:00 am)

C has to overtake also A exactly at 8:00 am and his speed is 30kmph (60kmphr - 30kmph = 30kmph and has to travel 60 kms).

60kms/30kmph = 2 hrs.

So C has so start at 6:00 am, so he would have started 6hrs after A who started at 00:00.

Im so confused,please explain.

Kind regards!
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Bunuel
Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 5

ar=30
br=40
kr=60

r=d/t
same direction = subtract rates

In 2hrs 'a' traveled 2*30=60km
Time for b to meet 'a': 60/(40-30)=6/1=6hrs
Time for k to meet 'a': 60/(60-30)=6/3=2hrs
Since b took 6 hrs to meet 'a', then k took (6-2)=4hrs.

Ans (C)
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Bunuel
Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 5


Are You Up For the Challenge: 700 Level Questions

We can create the equation:

40t = 30(t + 2)

40t = 30t + 60

10t = 60

t = 6

We see that Arun has traveled 30(6 + 2) = 30(8) = 240 miles. Barun has traveled the same distance, too (notice that 40(6) = 240), when he catches up with Arun. That will be the case with Kiranmala as well. That is, Kiranmala has traveled 240 miles when she catches up with Arun. Since it takes Kiranmala 240/60 = 4 hours to travel 240 miles and it takes Arun 8 hours to do so, she started 8 - 4 = 4 hours after Arun.

Answer: C

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Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

--> Distance travelled by all 3 is same. Hence, speed is inversely proportional to T. Let t be the time when A is overtaken by B and K.
Case 1:
30/40= (t-2)/t
t=8 hours
Case 2:
30/60=1/2= (8-n)/8
From options, n=4
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