A person has to cover a distance of 8km in 1 hour. If he covers one-fourth of the distance in one-third of the total time, then what should his speed (in km/h ) be to cover the remaining distance in the remaining time so that the person reaches the destination exactly on time?

Correct option is D

​Given:

Total distance = 8 km
Total time = 1 hour

Formula Used:

​$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$​​

Solution:

​$$\text{Distance covered in one-third of the time:}\\ \ \\ \frac{1}{4} \times 8 = 2 \, \text{km} \\\ \\\text{Time taken for this part:} \\\ \\\frac{1}{3} \times 1 = \frac{1}{3} \, \text{hour} \\\ \\\text{Remaining distance and time:} \\\ \\\text{Remaining distance} = 8 - 2 = 6 \, \text{km} \\\ \\\text{Remaining time} = 1 - \frac{1}{3} = \frac{2}{3} \, \text{hour} \\\ \\\text{Required speed:} \\\ \\\text{Speed} = \frac{\text{Remaining distance}}{\text{Remaining time}} = \frac{6}{\frac{2}{3}} = 6 \times \frac{3}{2} = 9 \, \text{km/h} \\\ \\$$​​