Moderate Time, Speed & Distance Solved QuestionAptitude Discussion

Common Information

$A$ and $B$ go by Bus from $X$ to $Z$ which is on the way to $Y$. $C$ goes from $Y$ to $Z$ by Auto. $A$ and $B$'s Bus goes at 75km/hr and $C$'s auto moves at 15 km/hr. All the three start at 6:00 am. After travelling some distance, $B$ sees another friend $D$ going by Cycle at  25km/hr to $Z$. $B$ and $A$ go ahead, meet $C$ and pick him up. They return immediately to $Z$ at the same time. The distance between $X$ and $Y$ is 600 km and $XZ$ is 400 km.

 Q. Common Information Question: 1/2 What is the total distance travelled by $A$?
 ✖ A. 480 km ✖ B. 450 km ✖ C. 550 km ✔ D. 600 km

Solution:
Option(D) is correct

$A$ and $B$'s speed is 5 times $C$'s speed. So $A$ and $B$ will travel 5 times than $C$ in the same time.

As $XZ=400$ km and $XY$ = 600 km they will meet at some point $V$, 500 km from $X$.

It is shown below:

$X$-------->-----------$Z$ ----->------ $V$--------<---------$Y$

$C$ covers 100 km by the time they meet at $V$. $A$, $B$ and $C$ then cover 100 km to come back to $Z$.

$A$ (as well as $B$) covers $(XZ+ZV+VZ=400+100+100)$ = 600 km.