If P : Q : R = 5 : 3 : 6, then what will be the ratio of P/Q : Q/R : R/P?

Shortcut Trick

P : Q : R = 5 : 3 : 6

Le P be 5x, Q be 3x and R be 6x

Then, (P/Q) ∶ (Q/R) ∶ (R/P) = (5x/3x) ∶ (3x/6x) ∶ (6x/5x)

Let us take the LCM (3, 6, 5) = 30

So, (P/Q) ∶ (Q/R) ∶ (R/P) = (5x/3x) × 30 ∶ (3x/6x) × 30 ∶ (6x/5x) × 30

∴ Required ratio is 50 ∶ 15 ∶ 36

Alternate Method

Given:

P : Q : R = 5 : 3 : 6

Le P be 5x, Q be 3x and R be 6x.

Concept:

If N is divided into a : b, then

First part = N × a/(a + b)

Second part = N × b/(a + b)

Calculations:

The required ratio = P/Q : Q/R : R/P

Multiplying the above ratio with PQR

⇒ Required ratio = P²R : Q²P : R²Q

Putting values of P,Q and R in above ratio, we get

⇒ Required ratio = (5x)²(6x) : (3x)²(5x) : (6x)²(3x)

⇒ Required ratio = (25x²)(6x) : (9x²)(5x): (36x²)(3x)

⇒ Required ratio = (25)(2) : (3)5: (36)

⇒ Required ratio = 50 : 15 : 36

∴ Required ratio is 50 ∶ 15 ∶ 36.