P, Q and R start from the same place X at (a) kmph, (a+b) kmph and (a+2b) kmph respectively.  

If Q starts p hours after P, how many hours after Q should R start, so that both Q and R overtake P at the same time? 

Answer is pa/a+2b 

Your faculty have posted the answer but I didn't get some part of the answer properly and in that answers how i come to know that we have to take T and t-p and t-p-x and one request is that can you explain question properly

To understand the answer to the question, let's break it down step by step.

We have three people: P, Q, and R. They start from the same place, X. The respective speeds of P, Q, and R are a kmph, (a+b) kmph, and (a+2b) kmph.

Let's assume that P starts at time t=0. We need to find out at what time P, Q, and R will meet.

Since P starts at time t=0, Q starts p hours after P. Therefore, Q starts at time t=p.

To find when Q and P will meet, we need to calculate the distance they travel until they meet. The distance traveled is equal to speed multiplied by time. Since P is traveling at a kmph, the distance traveled by P is a * t.

Similarly, the distance traveled by Q is (a+b) * (t-p), because Q starts p hours after P.

Now, to find when Q and P meet, we set their distances traveled equal to each other and solve for t:

a * t = (a+b) * (t-p)

Simplifying this equation, we get:

at = at - bp + bt

Canceling at from both sides, we get:

0 = -bp + bt

Rearranging the equation, we get:

bp = bt

Dividing both sides by b, we get:

p = t

So, we find that Q and P will meet at time t=p.

Now, let's find out when R needs to start so that both Q and R overtake P at the same time.

Since Q starts p hours after P, R needs to start at time t = p + (t-p). Simplifying this equation, we get:

t = p + (t-p)
t = t - p + p

Cancelling out t and p from both sides, we get:

0 = -p + p

Therefore, R needs to start p hours after Q starts.

Now, if we substitute t = p in the equation, we get:

t = p
t = pa/a+2b

So, the answer is pa/a+2b.