A walks at a uniform rate of 2 km/h and 2 h after his start,

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A walks at a uniform rate of 2 km/h and 2 h after his start, B cycles after him at the uniform rate of 5 km/h. How far from the starting point will B catch A?

1. 6²/₃ km
2. 6¹/₃ km
3. 6⁵/₇ km
4. 6³/₇ km

Correct Option: A

Let B catches A after T h.
Then, distance travelled by A in (T + 2) h = Distance travelled by B in T h

According to the question,
2 (T + 2 ) = 5T
⇒ 2T + 4 = 5T
⇒ 3T = 4
∴ T = 4/3 h

Distance travelled by B in 4/3 h
= (4/3) x 5 = 20/3 = 6²/₃ km