Question

State true or false:

Two consecutive whole numbers, the difference of whose reciprocals is $\frac{1}{12}$ are $3$ and $4$.

• A. True
• B. False

Answer 1

The correct option is A True

Let the two numbers be $a$ and $a+1$
$\frac{1}{a}-\frac{1}{a+1}=\frac{1}{12}$

$\frac{1}{a(a+1)}=\frac{1}{12}$

$12=a^2+a$
$a^2+4a-3a-12=0$
$(a+4)(a-3)=0$
$a=3,-4$
Neglecting the negative number, value of $a=3$.

$\therefore a+1=3+1=4$

Thus, the numbers are $3$ and $4$.