Question

If the sum of two numbersw is 27 and there hcft andr lcm are 3 and 60 respectively, then the sum of the reciprocal of the two number is?

Answer 1

$\color{Blue}Hello$☺!

$<b>Let the two numbers be x and y.$

By Given condition,
$<b>x+y=27 ◆x=27-y$

It is also given that,
$<b>HCF(x,y)=3,LCM(x,y)=60$

$<b>Now, LCM × HCF=xy$
$<b>60×3=xy$
Putting x=y-27
$<b>180=(27-y)y$
$<b>180=-y^2 +27 y$
$<b>y^2-27y+180=0$
$<b>(x-15)(x-12)=0$
$<b>x=15 or x=12.$
$<b>so y=12 or y=15$

Now sum of their reciprocals,
$<b>1/x +1/y=1/15 + 1/12$
$<b>=27/180$
$<b>1/x+1/y=3/20$

I hope this helps ☺.