Question

$a$, $\frac{1}{b}$, $c$ and $\frac{1}{d}$ are in proportion. Then,

• A. a×1d=1b×c
• B. a×1b=c×1d
• C. ab=c×1d
• D. a×1d=b×1c

Answer 1

The correct option is A a×1d=1b×c

Given that $a$, $\frac{1}{b}$, $c$ and $\frac{1}{d}$ are in proportion.
Then, by the rule of proportion, we have the product of extremes to be equal to the product of means.
$⟹a\times \frac{1}{d}=\frac{1}{b}\times c.......\left(1\right)$
Note that $\frac{1}{b}\times c\ne b\times \frac{1}{c}$ in general.
On cross multiplication of (1), we have $ab=cd$
Also, note that if $a$, $\frac{1}{b}$, $c$ and $\frac{1}{d}$ are in proportion, then $\frac{a}{\frac{1}{b}}=\frac{c}{\frac{1}{d}}$