Question

The L.C.M. and H.C.F of two numbers x and y are 3 and 105 respectively. If $x+y=36$, the value of $\frac{1}{x}+\frac{1}{y}$ is ___.

• A. 1
• B. $\frac{1}{6}$
• C. $\frac{12}{315}$
• D. $\frac{4}{35}$
• E. None of these

Answer 1

The correct option is D $\frac{4}{35}$

Multiple of two numbers = Multiple of L.C.M. and H.C.F. of that numbers
$\therefore xy=3\times 105\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}=\frac{36}{3\times 105}=\frac{12}{105}=\frac{4}{35}$