Ronit and Sonali is 50 km apart. When they move in opposite direction they meet in 5 hours. If Ronit moves at \(\frac{3}{4}\)th of his speed and Sonali at 1/4th of her speed then they meet in 8 hours 20 min . Find the speed of Ronit .

7 km/hr

Distance  =  Speed × Time

Distance = 50 km 

Time = 5 hours 

Speed = \(\frac{50}{5}\) = 10 km/hr 

Speed of ( ronit + sonali )  = 10 km/hr 

R + S = 10 km/hr   ------------ ( 1 ) 

Ronit moves at 3/4th of his speed and Sonali at 1/4th of her speed then they meet in 8 hours 20 min . 

8 hours 20 min = 8 + \(\frac{1}{3}\) = \(\frac{25}{3}\) hours

Speed = \(\frac{50 × 3}{25}\) = 6 km/hr 

\(\frac{3}{4}\)R + \(\frac{1}{4}\)S = 6 km/hr 

3R + 1R = 24 km/hr   ---------- ( 2 ) 

subtract equation ( 2 ) from ( 1 ) 

2R   =  14 km/hr 

1R   =   7 km/hr

Speed of Ronit = 7 km/hr