A car travelling with $$\frac{5}{7}$$ of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.

Solution (By Examveda Team)

Time taken :
$$\eqalign{ & = 1\,{\text{hr}}\,40\,{\text{min}}\,48\,{\text{sec}} \cr & = 1\,{\text{hr}}\,40\frac{4}{5}{\text{min}} \cr & = 1\frac{{51}}{{75}}{\text{hrs}} \cr & = \frac{{126}}{{75}}{\text{hrs}} \cr} $$
Let the actual speed be x km/hr
Then,
$$\eqalign{ & \frac{5}{7}x \times \frac{{126}}{{75}} = 42 \cr & {\text{Or }}x = \left( {\frac{{42 \times 7 \times 75}}{{5 \times 126}}} \right) \cr & x = 35{\text{ km/hr}} \cr} $$