The sum of two numbers is 36 and their H.C.F and L.C.M.

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The sum of two numbers is 36 and their H.C.F and L.C.M. are 3 and 105 respectively. The sum of the reciprocals of two numbers is

Let the numbers be 3p and 3q.
∴ 3p + 3q = 36
⇒ p + q = 12 ... (i)
and 3pq = 105 ... (ii)
Dividing equation (i) by (ii), we have

	p	+	q	=	12
	3pq		3pq		105

⇒	1	+	1	=	4
	3q		3p		35