Question

If $x$ is added to each of number $3,9,21$ so that the resulting numbers may be in G.P., then the value of $x$ will be

• A. $3$
• B. $\frac{1}{2}$
• C. $2$
• D. $\frac{1}{3}$

Answer 1

The correct option is A

$3$

Explanation for the correct option.

Form the equation and solve for $x$.

If $x$ is added to each of number $3,9,21$ then the numbers become $\left(3+x\right),\left(9+x\right),\left(21+x\right)$.

Now as the numbers $\left(3+x\right),\left(9+x\right),\left(21+x\right)$ are in G.P. so,

$$\begin{gathered} {\left(9+x\right)}^2=\left(3+x\right)\left(21+x\right) \\ \Rightarrow 81+18x+x^2=63+24x+x^2 \\ \Rightarrow 18=6x \\ \Rightarrow 3=x \end{gathered}$$

Thus the value of $x$ for which the numbers $\left(3+x\right),\left(9+x\right),\left(21+x\right)$ are in G.P. is $3$.

Hence, the correct option is A.