# Difficult Time, Speed & Distance Solved QuestionAptitude Discussion

 Q. $P$ and $Q$ travels from $D$ to $A$ and break journey at $M$ in between. Somewhere between $D$ and $M$, $P$ asks "how far have we travelled?" $Q$ replies, "Half as far as the distance from here to $M$". Somewhere between $M$ and $A$, exactly 300 km from the point where $P$ asks the first question, "How far have we to go?" $Q$ replies, "Half as far as the distance from $M$ to here". The distance between $D$ and $A$ is:
 ✖ A. 250 km ✖ B. 350 km ✔ C. 450 km ✖ D. 500 km

Solution:
Option(C) is correct

Let’s say it was point $Z$ when $P$ asked the first question and point $Y$ when $P$ asked the second question.

It can be shown as:

$D$----$Z$---->----$M$-------->--------$Y$--------$A$

Let $DM = x$ km, $MA = y$ km

Therefore, distance is $DA = DM + MA = x + y$

As per the information given in the question:

$ZY = 300$ km

Also

$ZM=\dfrac{2x}{3}\text{ and }MY=\dfrac{2y}{3}$

$â‡’ ZY = ZM + MY$

$=\dfrac{2x}{3}+\dfrac{2y}{3}$

$=300$

$⇒ x+y=450$ km

So distance between D and A is 450 km