Correct Answer - Option 4 : 1.6 km/h
Let VS and VF be the slower and faster speeds of train.
Now, according to question,
9 × VS = 5(2/5) × VF
⇒ VS/VF = 27/(9 × 5)
⇒ VS/VF = 3/5
Also, 4/VS - 4/VF = 1
⇒ (VF - VS/ VFVS) = 1/4
⇒ (1 - VS/VF)/VS = 1/4
⇒ VS = 4 × (1 – 3/5) = 4 × 2/5 = 8/5 = 1.6 km/h
⇒ VF = VS/(3/5) = 8/5/(3/5)= 8/3 = 2.6 km/h
slower speed is 1.6 km/h.