Question

If the sum of three numbers in G.P. is $63$ and the product of the first and the second term is $\frac{3}{4}$ of the third term, then the numbers are

• A. 3,12,48
• B. 4,12,36
• C. 2,10,50
• D. None of these

Answer 1

Answer: (A)

Let the three numbers be $a,ar,a{r}^2$
Given $a+ar+a{r}^2=63$
and $a\cdot ar=\frac{3}{4}\cdot a{r}^2$
or $a=\frac{3}{4}r$
Putting in (1), $\frac{3}{4}r+\frac{3}{4}r\cdot r+\frac{3}{4}r\cdot r^2=63$
or $r^3+r^2+r-84=0$
or$\therefore r=4,\frac{-5\pm \sqrt{25-84}}{2}$
$\therefore$ Real value of $r$ is $4$.
Putting this value in (2),
$a=\frac{3}{4}\times 4=3$
$\therefore$ The three numbers are, $3,3\times 4,3\times 4^2$,
i.e., $3,12,48$.