Rohan, Shikha's boyfriend, had to pick her from her home for a live concert on her 23^rd birthday. The venue of the concert and Shikha's home were in opposite directions from Rohan's office. He got late because of some work at office and realised that if he goes to pick Shikha from her home, which was a 48-minute drive from his office, they would be late for the show by 16 minutes. He asked her to start from her home towards his office in an auto-rickshaw and himself started driving towards her home. Both of them started simultaneously, he picked her as soon as they met and they managed to reach the venue just in time for the concert. If Rohan drives at an average speed of 60 km/hr, find the speed (in km/hr) of the auto-rickshaw.

A. 16 km

B. 20 km

C. 12 km

D. 15 km

E. None of these

Answer: Option C

Solution(By Examveda Team)

Let the speed of the rickshaw = S km/h. Let after time T they meet.
So, 60t + ST = $$\frac{{4 \times 60}}{5}$$ $$\left[ {{\text{Since,}}\,\,48\,{\text{min}} = \frac{4}{5}\,\,{\text{hour}}} \right]$$
Rohan saves 16 min. by making Shikha move as well. So, she saves 16 min by moving for distance X (Let).
2X = $$\frac{{60 \times 16}}{5}$$
X = 8 km
Speed of Auto rickshaw = 12 km. $$\left( {{\text{ST}} = 8\,{\text{km,}}\,\,{\text{T}} = \frac{2}{3}} \right)$$