SSC GD 2024 PYQ — Question 49

The correct answer is option 2 i.e. 144/7 km / h.

The total distance be ( D).

He covers half of the distance $\frac{D}{2}$, at a speed of 45 km/h.
Time taken for this part = $( \frac{\text{distance}}{\text{speed}} = \frac{\frac{D}{2}}{45} = \frac{D}{90} )$

 Remaining distance after the first part = $( \frac{D}{2} )$

40% of the remaining distance = $( 0.40 \times \frac{D}{2} = \frac{D}{5} )$

Time taken for this part = $( \frac{\frac{D}{5}}{8} = \frac{D}{40} )$

He covers this remaining distance at a speed of 24 km/h.
Time taken for this part = $( \frac{\frac{3D}{10}}{24} = \frac{3D}{240} = \frac{D}{80})$

Total time = $\frac{D}{90} + \frac{D}{40} + \frac{D}{80}$

⇒ $\frac{D}{90} = \frac{8D}{720}, \quad \frac{D}{40} = \frac{18D}{720}, \quad \frac{D}{80} = \frac{9D}{720}$
Total time = $\frac{8D}{720} + \frac{18D}{720} + \frac{9D}{720} = \frac{35D}{720}$

Average speed = $\frac{D}{\text{Total time}} = \frac{D}{\frac{35D}{720}} = \frac{720}{35} = \frac{144}{7}km/hr$