A man starts walking He walked 2 km in the first hour Then he walked two thirds of the distance of t...........

Quant (SSC) Time & distance

A man starts walking. He walked 2 km in the first hour. Then he walked two-thirds of the distance of the previous hour is each next hour. If he walked continuously then how long could he walk maximum?

60 km

6 km

12 km

8 km

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Explanation:

Reqd. distance
= [2 + 2 x 2/3 + (2 x 2/3)²+ (2 x 2/3)2 + .....∞]
If S_∞represents the sum of the ∞ terms of a geometric series
So, S_∞ = a + ar + ar² + ar³ + ar⁴ +.... + ∞
The sum to infinity is given by
S_∞ = a /1 - r only if –1 < r < 1
Here a = 2 and common ratio r = 2/3.
On putting the values, we get
= 2 × 1/ 1 - 2/3 = 2 × 3 = 6 km