Question

Choose the correct answers from the alternatives given.
The sum of two numbers is 36 and their H.C.F. and L.C.M. are 3 and 105 respectively. The sum of the reciprocals of two numbers is

• A. $\frac{2}{35}$
• B. $\frac{3}{25}$
• C. $\frac{4}{35}$
• D. $\frac{2}{25}$

Answer 1

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

Let the two numbers be x and y.
$\therefore$ x + y = 36
We know, Product of two numbers = H.C.F $\times$ L.C.M
x $\times$ y = L.C.M $\times$ H.C.F =3 $\times$ 105 = 315
Sum of reciprocals = $\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}=\frac{36}{315}\Rightarrow \frac{1}{x}+\frac{1}{y}=\frac{4}{35}$