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.
Similar Questions
Given that \(W : X = 5 : 6,\ X : Y = 3 : 7,\ \text{and}\ Y : Z = 8 : 9\), find the compound ratio \(W : X : Y : Z\).
Important Questions from Compound Ratios
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Rs. 750 are divided among A, B and C in such a manner that A : B = 5 : 2 and B : C = 7 : 13, What is B’s share?
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