Question

If $a,b,c,d$ are in $H.P.$ then the correct statement is :

• A. $ab>cd$
• B. $ac>bd$
• C. $ad>bc$
• D. $noneofthese$

Answer 1

The correct option is B $ac>bd$

With out loss generality let us assume that $a,b,c,d>0$ and $\frac{1}{a}<\frac{1}{b}<\frac{1}{c}<\frac{1}{d}$.

Then we have $a>b>c>d$.

So we have $a>b$......(1) and $c>d$.......(2).

From (1) we have,

$ac>bc$ [ Since $c>0$].....(3).

Again from (2) we get,

$bc>bd$ [ Since $b>0$]......(4).

From (3) and (4) we get,

$ac>bd$.