A journey of 96 km takes one hour less by a fast train (A) than by a slow train (B). If the average speed of B is 16 km/h less than that of A, then the average speed (in km/h) of A is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 48.
Speed = distance/time
Let the average speed of trains A and B be 'a' and 'b' respectively.
We have given that,
⇒ b = a - 16
The journey of 96 km takes one hour less by a fast train (A) than by a slow train (B)
⇒ 96/b - 96/a = 1
⇒ 1/b - 1/a = 1/96
⇒ 1/(a - 16) - 1/a = 1/96
⇒ 16/a(a - 16) = 1/96
⇒ a(a - 16) = 16 × 96
⇒ a2 - 16a - 1536 = 0
⇒ (a - 48)(a + 32) = 0
⇒ a = 48 km/h