Correct Answer - Option 1 : 48 km/h

Let T, A and B be the average speeds(km/h) of train, auto and bike respectively.

Given, T = 4A = 2.5B

⇒ A = T/4 and B = T/2.5 = 2T/5

According to question, 135/A + 780/T + 288/B = 17

⇒ 135/(T/4) + 780/T + 288/(2T/5) = 17

⇒ 540/T + 780/T + 720/T = 17

⇒ 2040/T = 17

⇒ T = 2040/17 = 120 km/h

Thus, B = 2T/5 = 0.4 × 120 = 48 km/h