You can use relative speed concepts here:
B starts 2 hrs after A so A covers 30*2 = 60 km in that time while B is still at starting point.

B makes up 10 km of relative distance every hour because the difference in their speed is 10 km/hr so it takes 60/10 = 6 hrs to cover additional 60 kms and overtake A. So B overtakes A in a total of 2+6 = 8 hrs since A started.

A will be 30*8 = 240 kms away from the starting point at this time. This is also the point where K overtakes A.
K will cover this distance in 240/60 = 4 hrs. So K must have started 8-4 = 4 hrs after A.

Answer (C)
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Mods - I don't know if I am allowed to provide a link to a youtube video explaining a distance/speed concept. If I am not, please let me know and I will delete my post.

I found a neat explanation of a concept that can be used to solve the type of question I posted earlier. For those interested, here it is
https://www.youtube.com/watch?v=Wqu1xKudqJQ

So, to solve this question, set up a table like this

B and K overtake in the same instant. So B overtake in (2*30)/(40-30) = 6 hours. That means B met after A went 8 hours.
So K starts after 30*8/60 = 4 hours

Could you please care to explain the equations?

You are most welcome to post any relevant links.

P.S. Image in your post does not show up.
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There was a typo in the screen grab earlier, so I took it down and posted a new one. Does the new one still doesn't show?

It's fine now. Thank you!
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Refer diagram below:



Speed of A = 30 km/hr

Speed of B = 40 km/hr

Stage I

B starts 2 hours after A, means that A has already travelled 60 Kms when B kicked off

Stage II

Say A further travels distance "x" where all 3 meet

Time taken by A to travel distance "x" = Time taken by B to travel distance "60+x"

\(\frac{x}{30} = \frac{60+x}{40}\)

4x = 3x + 180

x = 180

Total catch point distance = 60+180 = 240

Time required by A from start \(= \frac{240}{30} = 8 Hrs\)

Time required by K from start \(= \frac{240}{60} = 4 Hrs\)

Time difference between A & K = 8-4 = 4Hrs

Answer = C

I chose A because after getting 6h ( to over take A), I forgot to add the extra 2h, stupid mistake

After 2 hours A travels (t+2)30 km. When B catches up their distances are equal. Hence (t+2)30=40t ==> t=6. Now K is traveling 60 km and B is at 40 km. K needs (60/40) time less to catch up A. Hence K needs (6/(3/2))=4 hours. Hope it helps
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Hi all,

I need some help in understanding this problem. As you can see my answer comes close to 4 and in exam I would correctly "guess" ANSWER C and move on. But I am not understanding the rationale behind solution properly. Following is how I see it and I am stuck in this method of solving it. Can someone please help me?

TO

The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.
We know their rates are 30, 40 and 60.
Say the time taken by B is T hrs. Then A takes 2+T hrs. And we need to find the time taken by K.

Distance covered by A = Distance covered by B
30*(2+T) = 40*T
T = 6 hrs

Distance covered by B = Distance covered by K
40*T = 60*Time taken by K
Time taken by K = 40*6/60 = 4 hrs

Time taken by A = 2+T = 2+6 = 8 hrs
Time taken by K = 4 hrs
So K starts 8-4 = 4 hrs after A.
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One way to solve this problem.
A set off 2 hours prior to B. This implies A is 60 km ahead of B. So B will take 60/(40-30) hours=> 6 hours. Now B has travelled 6*40 = 240 kms. A can do 240 in 8. To do 240, K needs only 4 hours however. So K must have left 8-4 = 4 hours after A left.

My thought process if it helps anyone:

B and K overtake A at the same instant, this little phrase tells us everything we need to solve the question. This means that the distance traveled by A, B, and K are equal.

Let's say A travels for T hours. B started 2 hours after A, so that means B travels for T-2 hours.

Hence:

distance traveled by A = distance traveled by B

30t = 40(t-2)
t = 8

Total distance traveled by A, B and K = 240 kilometers. It takes K 4 hours to travel 240 km, hence K started 4 hours after A.

can you please explain how you got the 240km?

Rate of A = 30 km/hr

Let time of A = T hours

Rate of B = 40 km/hr

As per question, time of B = Time of A - 2 = T - 2 hours

Rate of K = 60 km/hr

Important : When two objects move from the same place in same direction and one object overtakes the other, they travel equal distance.

So, Distance travelled by A = Distance travelled by B (When B overtakes A)

30T = 40 (T - 2)

30 T = 40T - 80

T = 8

Now, Distance travelled by A = 30 * 8 = 240 kms

Distance travelled by B = 40 * 8 - 80 = 240 kms

Now question says B and K overtake A at the same time, means B and K have travelled the same distance,

Therefore, Distance travelled by K = 240 kms

Speed of K * Time of K = 240

60 * Time of K = 240

Time of K = 4 hours

Difference of time between A's and K's = 8 - 4

4 hours (C)

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The answer in the grab should end with 8-4 = 4. Time 4 hrs itself is not the answer as we need to know how many hours later did K start and not the time that K took to meet A.

It is just coincidence that both these times are 4 hours. Had these been different, the missing step would be necessary.

VeritasKarishma how is it possible that B overtakes A in 2+6 = 8 hrs 8 hours

B overtakes A in 6 hrs, it took only 6 hours to do the distance of 240 km for B to overtake A. While A did 60 km, B was not moving. So how can you attribute additional 2 hours to B ?

I° Step
If every hour it decreases the distance between A and B of 10km because of 40-30=10km:
Try with 6h:
B: 40km/h*6h=240
A: 60km+30km/h*6h=240 OK!
II° Step
K: 60km/h*x=240km
x=240km/60km/h -> 4h
III° Step
Now, if i know that K reaches A in 4h:
A=2h(60km) + 6h(180km)=8h(240km)
A-B=4h

Answer->C