Correct Option: B

Let the two men meet after t hours.

Distance covered by the first man starting from A = 4 t km.
Distance covered by the second man starting from B

= 2 + 2.5 + 3 +......+		2 +		t − 1
				2

This is an arithmetic series of t terms with 1/2 as common difference.
∴  By applying formula

S =	n		2a + (n − 1)d
	2

Where, n = no. of terms
a = first term
d = common difference
We have its sum

S =	t		(2 × 2) + (t − 1) ×	1
	2			2

= 2t +	t2 − t
	4

Total distance covered by two men =

= 4t + 2t +	t2 − t	= 72
	4

or

= 6t +	t2 − t	= 72
	4

or  24t + t² – t = 288
or  t² + 23t – 288 = 0
or  t² – 9t + 32t – 288 = 0
or  t (t–9) + 32 (t – 9) = 0
or  (t – 9) (t + 32) = 0
∴  Either t – 9 = 0 ⇒ t = 9
or  (t + 32) = 0 ⇒ t = – 32
Time cannot be negative.
Hence, the two men will meet after 9 hrs.