Chaining A : B and B : C again — Aptitude Question
Chaining A : B and B : C again: If A : B = 5 : 7 and B : C = 6 : 11, what is A : B : C? Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
If A : B = 5 : 7 and B : C = 6 : 11, what is A : B : C?
Options
- 30 : 42 : 77
- 35 : 42 : 66
- 5 : 7 : 11
- 30 : 42 : 66
Show the answer and the worked solution
Correct answer: A. 30 : 42 : 77
Worked solution
- A : B = 5 : 7 = 30 : 42 (multiply by 6).
- B : C = 6 : 11 = 42 : 77 (multiply by 7).
- So A : B : C = 30 : 42 : 77.
Answer: 30 : 42 : 77.
The idea
Scale each ratio by the other's value of the shared term. Here 7 × 6 = 42 does the job without needing the LCM separately.
Shortcut. Check C : B = 11 : 6 in each option: 77 : 42 = 11 : 6, while 66 : 42 = 11 : 7. With 30 : 42 = 5 : 7 as well, 30 : 42 : 77 is the only fit.
Common trap. "30 : 42 : 66" — scaling the second ratio by 6, like the first, instead of by 7; 42 : 66 is 7 : 11, not 6 : 11.