Ravi walks to and fro to a shopping mall. He spends 30 minutes shopping. If he walks at a speed of 10 km an hour, he returns home at 19.00 hours. If he walks at 15 km an hour, her returns home at 18.30 hours. How far must he walk in order to return home at 18.15 hours ?

Solution(By Examveda Team)

Let the to and fro distance to the mall be x km
Then,
$$\eqalign{ & \Rightarrow \frac{x}{{10}} - \frac{x}{{15}} = \frac{{30}}{{60}} \cr & \Rightarrow \frac{x}{{10}} - \frac{x}{{15}} = \frac{1}{2} \cr & \Rightarrow \frac{x}{{30}} = \frac{1}{2} \cr & \Rightarrow x = 15 \cr} $$
. Time taken to travel 15 km at 10 km/hr
$$\eqalign{ & = \left( {\frac{{15}}{{10}}} \right){\text{ hr}} \cr & = \frac{3}{2}{\text{ hr}} \cr & = 1\frac{1}{2}{\text{ hrs}} \cr} $$
Since 30 minutes were spent in shopping, so Ravi started for the mall 2 hours before 19.00 hrs i.e., at 17.00 hrs
Now, required time for to and fro journey :
$$\eqalign{ & {\text{ = }}\left( {18.15{\text{ hrs}} - 17.00{\text{ hrs}}} \right) - 30{\text{ min}} \cr & {\text{ = 45 min}} \cr & {\text{ = }}\frac{3}{4}{\text{ hrs}} \cr} $$
Hence, required speed :
$$\eqalign{ & {\text{ = }}\left( {15 \times \frac{4}{3}} \right){\text{ km/hr}} \cr & = 20{\text{ km/hr}} \cr} $$