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

Solution(By Examveda Team)

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