SSC GD 2024 PYQ — Question 44

The correct answer is option 1 i.e. 480/11 km/hr.

The usual time Aman takes to reach his office = ( t) hours.

The distance between Aman’s home and office = ( d ) kilometers.

⇒ d = $80 \left(t - \frac{1}{6}\right)$

The distance ( d ) in this case can be expressed as:

⇒ $d = 30 \left(t + \frac{1}{6}\right)$

⇒ $80 \left(t - \frac{1}{6}\right) = 30 \left(t + \frac{1}{6}\right)$
⇒ $80t - \frac{80}{6} = 30t + \frac{30}{6}$

⇒ $80t - \frac{40}{3} = 30t + 5$

⇒ 80t - 30t = 5 + 40 / 3
⇒ $50t = 5 + \frac{40}{3} = \frac{15}{3} + \frac{40}{3} = \frac{55}{3}$
⇒ t =  $\frac{\frac{55}{3}}{50} = \frac{55}{150} = \frac{11}{30}$ hours
⇒ d = $80 \left( \frac{11}{30} - \frac{1}{6} \right)$

⇒ $\frac{11}{30} - \frac{1}{6} = \frac{11}{30} - \frac{5}{30} = \frac{6}{30} = \frac{1}{5}$
⇒ d = 80 × (1)/(5) = 16 kilometerse

Speed = Distance / Time = $\frac{16}{\frac{11}{30}} = 16 \times \frac{30}{11} = \frac{480}{11}$ km/hr