Arun, Barun and Kiranmala start from the same place and travel in the

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!

given speeds as follows , A = 30kmph B = 40 kmph K = 60 kmph

As they meet Arun at same point the distance travelled is same.

for A, D = 30 * t
for B, D = 40* (t-2) as B takes 2hrs less to reach the same point,
For K D = 60 * (t-2-x) let x be the hrs when k starts after B, and he reaches the same point.

solving the 1 and 2 equation we t = 8 hrs and then we get x = 2hrs

so in total k starts after 2+2 = 4hrs

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!

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)

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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