Three numbers from two ratios — Aptitude Question
Three numbers from two ratios: The sum of three numbers is 98. The ratio of the first to the second is 2 : 3, and… Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
The sum of three numbers is 98. The ratio of the first to the second is 2 : 3, and of the second to the third is 5 : 8. What is the second number?
Options
- 20
- 30
- 48
- 58
Show the answer and the worked solution
Correct answer: B. 30
Worked solution
- First : second = 2 : 3 = 10 : 15; second : third = 5 : 8 = 15 : 24.
- So the three are in the ratio 10 : 15 : 24, giving 49 parts.
- One part = 98 ÷ 49 = 2, so the second number = 15 × 2 = 30.
Answer: 30.
The idea
Scale both ratios so the shared middle term agrees, then share the total. The clean part count (49 into 98) confirms the scaling was right.
Shortcut. With the numbers in 10 : 15 : 24 (49 parts), the second is 15/49 of 98 = 15 × 2 = 30.
Common trap. "20" — sharing 98 correctly but taking the first number's 10 parts instead of the second's 15.