If P : Q = 6 : 11, Q : R = 5 : 4, and R : S = 9 : 7, find P : Q : R : S.
270 : 495 : 396 : 308
Step 1 – Equalise Q across the first two ratios:
\(P : Q = 6 : 11 \quad\text{and}\quad Q : R = 5 : 4\)
Multiply P:Q by 5 and Q:R by 11 so that Q is common (= 55):
\(P : Q = 30 : 55,\quad Q : R = 55 : 44 \;\Longrightarrow\; P : Q : R = 30 : 55 : 44\)
Step 2 – Equalise R with the third ratio:
\(R : S = 9 : 7,\;\text{but our R} = 44.\)
Multiply R:S by \(\tfrac{44}{9}\) (i.e. scale all four numbers by 9):
\(P : Q : R = 270 : 495 : 396,\quad R : S = 396 : 308\)
Step 3 – Combine:
\(P : Q : R : S = 270 : 495 : 396 : 308\)
Hence the answer is option 1.
Given that \(W : X = 5 : 6,\ X : Y = 3 : 7,\ \text{and}\ Y : Z = 8 : 9\), find the compound ratio \(W : X : Y : Z\).
If A : B = 2 : 5, B : C = 4 : 3 and C : D = 2 : 1, then what is value of A : C : D?
The following ratios are given:
\(a : b = 2 : 3\)
\(b : c = 4 : 5\)
\(c : d = 3 : 2\)
\(d : e = 5 : 4\)
What is the value of the ratio a : e?
If (x + 2) is a common factor of x 2+ ax + b and x 2+ bx + a, then the ratio of a ∶ b is equal to
Rs. 2420 were divided among A, B, C so that A : B = 5 : 4 and B : C = 9 : 10 then C gets: