CAT 2018 Question Paper Shift 1 Solved Paper

Question : 67 of 100

Marks: +1, -0

Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is

$3/5$
$1/6$
$3/6$
$5/2$

Validate

Solution:

Since

x, y,

and

z

are in G.P. and $x 0

a n d

r > 1$
It is also given that,

15 {x}, 16 {y}

and

12 {z}

are in

{A} . {P}

.
Therefore,

2 × 16 {y}=5 {x}+12 {z}

Substituting the values of

{x}, {y}

and

{z}

we get,

32 a r=5 a+12 a r^{2}

⇒ 32 r=5+12 r^{2}

⇒ 12 r^{2}-32 r+5=0

On solving the above quadratic equation we get

r=1 / 6

5 / 2

.
Since

{r}>1

, therefore

{r}=5 / 2

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