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?

Distance = $$ speed \times time = 50\times 8 = 400 km $$

speed of Rahman =$$\dfrac{dist}{time} = \dfrac {400}{5} = 80 \dfrac{km}{hr}$$

new speed of Ranjeet = $$50+10 = 60 \dfrac{km} {hr}$$

new speed of Rahman = $$80 + 20 =100 \dfrac {km}{hr}$$

Time taken by Ranjeet with new speed = $$ \dfrac {400}{60} = \dfrac {20}{3} hr $$

Time taken by Rahman with new speed = $$ \dfrac {400}{100} = 4 hr $$

then difference both speed = $$\dfrac {20}{3} - 4 = \dfrac {20-12}{3} =\dfrac {8}{3}hr$$

$$\Rightarrow 2\dfrac {2}{3} hr $$

$$\Rightarrow 2  hr  and  \dfrac {2}{3} \times   60 min $$

$$\Rightarrow 2$$  hr  and  40 min Ans