Question

the H.C.F. and L.C.M. of two numbers x and y are 2 and 16 respectively.if x+y=18,then the value of 1/x+1/y is options are 16/9,3/2,8 and 9/16

Answer 1

Answer:

ur answer is;9/16

please refer to the attached picture

I hope it would help you

thank you

Answer 2

Given: HCF and LCM of two numbers $x$ and $y$ are 2 and 16 respectively

           and  $x + y = 18$

To find: The value of $\frac{1}{x} \ + \ \frac{1}{y}$

Solution: According to the given question,

HCF of $x$ and $y$ = 2

LCM of $x$ and $y$ = 16

and $x + y = 18$   ...(1)

We know that,

∵ Product of two numbers = Product of their HCF and LCM

∴ $xy = 2 \ * \ 16 = 32$  ...(2)

Now,

∵ $\frac{1}{x} \ + \ \frac{1}{y} = \frac{y \ + \ x}{xy}$

⇒ $\frac{18}{32} \ or \ \frac{9}{16}$                   [from (1) and (2)]

Hence, $\frac{1}{x} \ + \ \frac{1}{y} = \frac{9}{16}$