Question

$\text{If}\frac{31}{9}=P\frac{Q}{R}\text{, calculate the value of the}\text{expression,}Q\frac{(P+2)}{R}-Q\frac{P}{R}$

• A. $\frac{1}{9}$
• B. $\frac{2}{9}$
• C. $\frac{4}{9}$
• D. $\frac{5}{9}$

Answer 1

The correct option is B $\frac{2}{9}$

$\text{We know that}\frac{31}{9}=P\frac{Q}{R}$

$⟹P\frac{Q}{R}=\frac{(27+4)}{9}=3+\frac{4}{9}=3\frac{4}{9}$

$\therefore P=3;Q=4;R=9$

$⟹Q\frac{(P+2)}{R}-Q\frac{P}{R}=4\frac{(3+2)}{9}-4\frac{3}{9}=4\frac{5}{9}-4\frac{3}{9}=\frac{(4\times 9)+5}{9}-\frac{(4\times 9)+3}{9}=\frac{41}{9}-\frac{39}{9}=\frac{(41-39)}{9}=\frac{2}{9}$

$\therefore Q\frac{(P+2)}{R}-Q\frac{P}{R}=\frac{2}{9}$