NIELIT 2022 Feb Scientist D - Section D: 16

Question

A positive number when decreased by $4$ is equal to $21$ times the reciprocal of the number. The number(s) is/are :

• A. $3$
• B. $7$
• C. $3$ and $-7$
• D. $-3$ and $7$

Answer 1

Let the positive number be $x$.

so $x-4=\frac{21}{x}$

$\implies x(x-4)=21$

$\implies x^2-4x-21=0$

$\implies x^2-7x+3x-21=0$

$\implies x(x-7)+3(x-7)=0$

$\implies (x-7)(x+3)=0$

$\implies x=7,-3$

Option (D) is correct.