Question

The sum of two numbers is 36 and their h.c.f and lcm are 3 and 105 respectively.the sum of the reciprocals of two numbers is

Answer 1

let the numbers be x and y say

x+y=36

lcm=105; hcf=3

x×y=lcm×hcf

xy=105×3=315

sum of the reciprocals of two numbers is

1/x+1/y=(y+x)/xy

=36/315

=4/35

xy=

Answer 2

Answer:

Let two numbers be x and y.

As per the given condition;

the sum of two numbers is 36 i.e, x+y =36      ......[1]

LCM of two numbers x and y is the Least Common Multiple

and the  HCF of two numbers is the Highest Common Factor.

The product of the LCM and HCF of two numbers is the same as the product of the numbers themselves i.e

$LCM \times HCF =x \times y$

Given;

HCF =3 and LCM =105

then;

$x \times y = 3 \times 105 = 315$ or

$x \times y =315$                                      ......[2]

To find the sum of the reciprocals of two numbers :

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

or

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

=$\frac{36}{315}= \frac{4}{35}$     [using [1] & [2] ]

Therefore, the reciprocals of two numbers is; $\frac{4}{35}$