Question

Train A running at $60$ km/h leaves Mumbai for Delhi at $6$ p.m. Train B running at $90$ km/h also leaves for Delhi at $9$ p.m. Train C leaves Delhi for Mumbai at $9$ p.m. If all three trains meet at the same time between Mumbai and Delhi (distance $=1260$ km), find the speed of Train C.

• A. $60$ km/h
• B. $90$ km/h
• C. $120$ km/h
• D. $135$ km/h

Hint:

First fix the meeting time and location using any two movers. Then use that location and remaining time window to determine the third mover's speed.

Answer 1

The Correct Option is C

Step 1: Let the common meeting time be $t$ hours after 6 p.m.
Position of A from Mumbai: $x_A=60t$.
Position of B from Mumbai (starts $3$ h later): $x_B=90(t-3)$. 

Step 2: A and B must be at the same point at the meeting time.
$60t=90(t-3)\Rightarrow 60t=90t-270\Rightarrow t=9$ h.
Meeting clock time $=3$ a.m.; location from Mumbai $=60\times 9=540$ km. 

Step 3: Use Train C's travel from Delhi.
Distance from Delhi to meeting point $=1260-540=720$ km.
Time available for C (from 9 p.m. to 3 a.m.) $=t-3=6$ h.
\[ \text{Speed of C}=\frac{720}{6}=120\ \text{km/h}. \] \[ \boxed{120\ \text{km/h}} \]