Question 126

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

Solution

let's say numbers are $$x$$ and $$y$$
hence sum of the reciprocals will be $$\frac{1}{x} + \frac{1}{y}$$
or $$\frac{x +y}{xy}$$
as $$x+y$$ = 36 (given)
and $$xy$$ = $$HCF \times LCM$$
= $$3 \times 105 = 315$$
after putting the values we will get summation of reciprocals equals to $$\frac{4}{35}$$

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