Correct Option: D

Relative speed of insect
= 30 + 42 = 72 km per hr.
Distance between railway engine and insect = 20 km.
Engine and insect will meet for the first time after

=	20	hr.
	72

Distance covered in this period

=	20	× 42 =	35	km
	72		3

The insect will cover	35	km in returning to A.
	3

The distance covered by engine in this period

=	20	× 30 =	25	km
	72		3

Since, the insect when reaches A,

the engine will cover	25	to A.
	3

∴  Remaining distance between A and engine

= 20 −		25	+	25
		3		3

Again, engine and insect will meet after	10	=	5	hr.
	3 × 72		108

The distance covered by the insect in this period

=	5	× 42 =	35	km
	108		18

tand again the insect will cover	35	km in returning.
	18

∴ Total distance covered by the insect =	70	+	70	+.....
	3		18

=	70		1 +	1	+.......∞
	3			6

It is a Geometric Progression to infinity with common ratio 1/6.

=	70		1
	3		1 − (1/6)

	∴  S∞ =	a
		1 − r

=	70	×	1
	3		(5/6)

=	70	×	6	= 28 km
	3		5