Question

Two cars start out simultaneously from a point in the same direction, one of them going at a speed of $50$ $km/hr$ and the other at $40$ $km/hr$. In half an hour a third car starts out from the same point and overtakes the first car $1.5$ hours after catching up with the second car. The speed of the third car is

• A. $72km/hr$
  
• B. $90km/hr$
  
• C. $55km/hr$
  
• D. $60km/hr$

Answer 1

The correct option is D $60km/hr$

Positions of the cars when third car starts is shown.
Let third car catches $2^{nd}$ car after time $T$ it starts out.
$vT=40T+20\dots \left(i\right)$
Now third car catches $1^{st}$ car after time $T+\mathrm{1.5.}$
$\text{So}v[T+1.5]=50[T+1.5]+25\dots \left(ii\right)$
Put the value of T from equation $\left(i\right)$ into equation $\left(ii\right)$, we get
$1.5v^2-140v+3000=0$
$3v^2-280v+6000=0$
$v=\frac{280\pm \sqrt{(280{)}^2-72000}}{6}$
$\Rightarrow v=\frac{280\pm 80}{6}$
$=60km/hr,\frac{100}{3}$ $km/hr$
As $v$ cannot be less than $50km/hr$
Final Answer: (b)