Correct Option: A

Let the total distance travelled be x kms.
Case I :
Speed for the first one-third distance

i.e.	x	kms =10 km per hr.
	3

∴  Time taken =	x	hours
	30

Similarly, time taken for the next one-third distance

=	x	hours
	27

and time taken for the last onethird distance

=	x	hours.
	24

∴  Total time taken to cover x kms.

=		x	+	x	+	x		hours.
		30		27		24

Case II :
Time taken for one-half distance at the speed of 10 km per hr.

=	x	hrs.
	20

and time taken for remaining 1/2 of distance

=	x	hrs. at 8 km per hr.
	16

Total time taken =		x	+	x		hrs.
		20		16

Time taken in (Case II – Case I)

= 1 minute =	1	hr.
	60

∴  According to the question

x	+	x	−		x	+	x	+	x
20		16			30		27		24

=	1
	60

⇒	108x + 135x − 72x − 80x − 90x
	2160

=	1
	60

⇒	243x − 242x	=	1
	2160		60

⇒	x	=	1
	2160		60

⇒  x =	2160	= 36 km.
	60

Hence the required distance
= 36 km.