Question

The sum of two numbers is $55$ and the HCF and LCM of these two numbers are $5$ and $120$ respectively. Find the sum of reciprocals of these numbers.

Answer 1

Let assume the two given numbers are $x$ and $y$ respectively.

It is given that,

The sum of two numbers is $55$

it implies,

$x$ $+$ $y$ $=$ $55$

HCF and LCM of these two numbers are $5$ and $120$ respectively.

Note :

The product of two given numbers $=$HCF $\times$LCM .

So,

The Product of two given numbers $=$ $5\times 120$

$=$$600$

i.e. $xy=600$

The sum of the reciprocals of two given numbers is $\frac{1}{x}+\frac{1}{y}$

then,

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

$\frac{1}{x}+\frac{1}{y}=\frac{55}{600}$

$\frac{1}{x}+\frac{1}{y}=\frac{11}{120}$.

Hence, the sum of the reciprocals of two given numbers is $\frac{11}{120}$.