A ratio of two expressions — Aptitude Question
A ratio of two expressions: If a : b = 3 : 4, what is (2a + 3b) : (3a + 2b)? Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 50 seconds
Question
If a : b = 3 : 4, what is (2a + 3b) : (3a + 2b)?
Options
- 17 : 18
- 18 : 17
- 5 : 6
- 6 : 5
Show the answer and the worked solution
Correct answer: B. 18 : 17
Worked solution
- Take a = 3, b = 4.
- 2a + 3b = 6 + 12 = 18; 3a + 2b = 9 + 8 = 17.
- The ratio is 18 : 17.
Answer: 18 : 17.
The idea
Substitute and compute. Keep the order the question asks for — 17 : 18 is offered for anyone who writes the two lines the wrong way round.
Shortcut. The two expressions add to 5(a + b) = 35 and differ by b − a = 1, so they are 18 and 17, the first the larger.
Common trap. "17 : 18" — getting 18 and 17 but writing them in the wrong order.