Question

State true or false:

Two consecutive natural numbers, the sum of whose reciprocals is $\frac{11}{30}$ are $5$ and $6$.

• A. True
• B. False

Answer 1

The correct option is A True

Let the two consecutive natural numbers be $a$ and $a+1$
Sum of their reciprocals is

$\frac{1}{a}+\frac{1}{a+1}=\frac{11}{30}$

$\frac{a+a+1}{a\times (a+1)}=\frac{11}{30}$

$60a+30=11a^2+11a$
$11a^2-49a-30=0$
$11a^2-55a+6a-30=04$
$11a(a-5)+6(a-5)=0$

$a=5,\frac{-6}{11}$

Neglecting negative fraction, value of $a=5$.

$\therefore a+1=5+1=6$

Hence the numbers are $5$ and $6$