Question

The hcf and lcm of two numbers x and y are respectivaly 3 and 105.If x+y=36 then 1/x+1/y=

Answer 1

Answer: 4/35

hcf(x,y) = 3

lcm(x,y) = 105

Since, hcf(x,y)*lcm(x,y) = x*y

xy= 105*3= 315

Therefore, 1/x+1/y=(x+y)/xy=36/315=4/35

Answer 2

The value is $\frac{1}{x}+\frac{1}{y}=\frac{4}{35}$

Step-by-step explanation:

Given : The hcf and lcm of two numbers x and y are respectively 3 and 105. If x+y=36.

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

Solution :

We know that,

$\text{Product of two numbers}=\text{HCF}\times \text{LCM}$

HCF = 3, LCM = 105 and two numbers are x and y

$xy=3\times 105$

$xy=315$ .....(1)

$x+y=36$ .....(2)

Solving expression as,

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

$\frac{1}{x}+\frac{1}{y}=\frac{36}{315}$

$\frac{1}{x}+\frac{1}{y}=\frac{4}{35}$

Therefore, the value is $\frac{1}{x}+\frac{1}{y}=\frac{4}{35}$

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