If P : Q = 7 : 4 and Q : R = 5 : 14, find (i) R : P (ii) P : Q : R.

Given,

P : Q = 7 : 4

Q : R = 5 : 14

To find R : P and P : Q : R, we will make Q same in both cases.

Taking L.C.M of two values of Q i.e. 4 and 5 = 20

So, $\dfrac{P}{Q} = \dfrac{7 \times 5}{4 \times 5} = \dfrac{35}{20}$ = 35 : 20

and $\dfrac{Q}{R} = \dfrac{5 \times 4}{14 \times 4} = \dfrac{20}{56}$ = 20 : 56

$\Rightarrow \dfrac{P}{Q} \times \dfrac{Q}{R} = \dfrac{35}{20} \times \dfrac{20}{56} \\[1em] \Rightarrow \dfrac{P}{R} = \dfrac{35}{56} \\[1em] \Rightarrow \dfrac{P}{R} = \dfrac{5}{8} \\[1em] \Rightarrow \dfrac{R}{P} = \dfrac{8}{5}.$

Hence, R : P = 8 : 5.

∴ P : Q : R = 35 : 20 : 56

Hence, ratio of P : Q : R = 35 : 20 : 56.