If P : Q : R = 2 : 3 : 4, then find: $\frac{P}{Q}:\frac{Q}{R}:\frac{R}{P}$.

8 : 9 : 24

The correct answer is Option (2) → 8 : 9 : 24

Given

$P : Q : R = 2 : 3 : 4$

So, let

$P = 2k,\quad Q = 3k,\quad R = 4k$

Now compute:

• $\frac{P}{Q} = \frac{2k}{3k} = \frac{2}{3}$​
• $\frac{Q}{R} = \frac{3k}{4k} = \frac{3}{4}$​
• $\frac{R}{P} = \frac{4k}{2k} = 2$

So,

$PQ : QR : RP = \frac{2}{3} : \frac{3}{4} : 2$

To remove fractions, multiply all by 12:

$8 : 9 : 24$