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Question

If P : Q = 6 : 11, Q : R = 5 : 4, and R : S = 9 : 7, find P : Q : R : S.

This question was previously asked in
SSC CGL 2025 Tier 2 Paper 1 Question Paper (19-Jan-2026)
The correct answer is

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.

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