Question

Pallavi and Richa start simultaneously from $P\,\,and\,\,Q$towards $Q\,\,and\,\,P$ respectively. They meet on the way at$T$, which is at a distance of $120m$ from$P$. If Pallavi and Richa take $16s\,\,and\,\,25$ to reach their respective destinations from $T$, then what is the distance between $P$and $Q$
A. $214m$
B. $200m$
C. $240m$
D. $216m$

Answer 1

Hint: This question is basically related to the simple theory of speed, distance and time.
By using formula: $speed = \dfrac{{dis\tan ce\,\,travel}}{{time\,\,taken}}$
Basic definition of speed:
The speed of any entity/object/person is the magnitude of the change of its position.


Complete step by step solution:
In our question
It given that,
\[\mathop {\mathop {\mathop P\limits^ \bullet \,}\limits_{Pallavi} }\limits^ \to \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mathop T\limits^ \bullet \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mathop {\,\,\mathop {\,\mathop Q\limits^ \bullet \,}\limits_{Richa} }\limits^ \leftarrow \]

Pallavi starts from $P$ towards $Q$
Richa starts from $Q$ towards $P$
Distance between points $P$ and $T$ is $120m$.
When both meets at point $T$,
After that,
Richa travels $120m\,\,to\,\,reach\,\,po\operatorname{int} \,\,P\,\,in = 25\sec $
By using the speed formula,
$speed = \dfrac{{dis\tan ce\,\,travel}}{{time\,\,taken}}$
So, speed of Richa $ = \dfrac{{120}}{{25}} = 4.8m/\sec $
Time of Pallavi $ = 25\sec $
Time of Richa $ = 16\sec $
Now, Speed of Pallavi divided by speed by Richa $ = \dfrac{{25}}{{16}} = \dfrac{5}{4}\sec $
$\therefore $ Speed of Pallavi $ = \dfrac{5}{4} \times 4.8m/\sec $
Speed of Pallavi $ = 6m/s$
As, Pallavi takes $16$ seconds to travel from $T$ to $Q$
By using the distance formula
$Dis\tan ce = Speed*Time$,
Here, $Speed = 6m/\sec ,time = 16\sec $
So, Distance from $T$to $Q$is
$
   = (16 \times 6)m \\
   = 96m \\
 $
Total distance between $P\,\,and\,\,Q\,\,is$$ = (120 + 96)m$
Total distance between $P\,\,and\,\,Q\,\,is$$ = 216m$
Hence, the correct option is D.


Note: It is a simple problem of aptitude and reasoning involving very basic and elementary concepts of speed, distance and time.
So, while solving these types of questions, always make sure to write the appropriate Si unit associated with the final answer