Question

Given that a, b, c, d, p and q are natural numbers such that a < b and d < c and q < p and given that $\frac{a}{b}\times \frac{d}{c}=\frac{q}{p}$ holds true,Which of the following is/are true?

• A. $q<p$
• B. $q>p$
• C. $\frac{a}{b}<\frac{q}{p}and\frac{d}{c}<\frac{q}{p}$
• D. $\frac{a}{b}>\frac{q}{p}and\frac{d}{c}>\frac{q}{p}$

Answer 1

The correct option is D

$\frac{a}{b}>\frac{q}{p}and\frac{d}{c}>\frac{q}{p}$

$\frac{a}{b}\times \frac{d}{c}=\frac{q}{p}$
here, $\frac{a}{b}>\frac{q}{p}and\frac{d}{c}>\frac{q}{p}andq<p$
For eg,
$\frac{2}{3}\times \frac{5}{6}=\frac{10}{18}$
here, $\frac{2}{3}>\frac{10}{18}(as\frac{12}{18}>\frac{10}{18})$
and $\frac{5}{6}>\frac{10}{18}(as\frac{15}{18}>\frac{10}{18})$
also, $10<18$