Ranjeet drives his car at an average speed of 50 km/hr and reaches his destination in 8 hours. Rahman covers the same distance in 5 hours. If Ranjeet increases his speed by 10 km/hr and Rahman increases his speed by 20 km/hr, then what will be the difference in time taken by them to reach their destination?

2 hours 40 minutes

Distance = Speed × Time `

Total distance covered by Ranjeet in 8 hrs = 50 × 8 = 400 km

Speed of Rahman = \(\frac{400}{5}\) = 80 km/hr

New speed of Ranjeet = 50 + 10 = 60 km/hr

Time taken by Ranjeet to cover 400 km distance = \(\frac{400}{60}\)= 6 hr 40 min

New speed of Rahman = 80 + 20 = 100 km/hr

Time taken by Rahman to cover 400 km distance = \(\frac{400}{100}\) = 4 hr

Required difference = 6 hr + 40 min – 4 hr

= 2 hours 40 minutes