From p : q and q : r to p : r — Aptitude Question
From p : q and q : r to p : r: If p : q = 3 : 4 and q : r = 8 : 9, what is p : r? Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
If p : q = 3 : 4 and q : r = 8 : 9, what is p : r?
Options
- 1 : 2
- 2 : 3
- 3 : 4
- 4 : 9
Show the answer and the worked solution
Correct answer: B. 2 : 3
Worked solution
- p/r = (p/q) × (q/r) = (3/4) × (8/9) = 24/36 = 2/3.
- So p : r = 2 : 3.
Answer: 2 : 3.
The idea
When only the two outer terms are wanted, multiply the fractions and skip building the full three-term ratio.
Shortcut. Scale p : q so that q matches: 3 : 4 = 6 : 8, and q : r = 8 : 9, so p : r = 6 : 9 = 2 : 3.
Common trap. "3 : 4" — it looks right because q : r = 8 : 9 is close to 1, but copying p : q ignores that factor; (3/4) × (8/9) = 2/3.