Sharing in a fractional ratio — Aptitude Question
Sharing in a fractional ratio: ₹782 is divided among three people in the ratio ½ : ⅔ : ¾. What is the first share? Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
₹782 is divided among three people in the ratio ½ : ⅔ : ¾. What is the first share?
Options
- ₹182
- ₹190
- ₹204
- ₹272
Show the answer and the worked solution
Correct answer: C. ₹204
Worked solution
- Multiply by 12: ½ : ⅔ : ¾ = 6 : 8 : 9.
- Total parts = 23, so one part = 782 ÷ 23 = ₹34.
- First share = 6 × 34 = ₹204.
Answer: ₹204.
The idea
Never share out fractions directly. Multiply through by the LCM of the denominators first, then treat it as an ordinary whole-number ratio.
Shortcut. Every share is a whole number of ₹34 parts (782 ÷ 23 = 34), so only ₹204 (6 × 34) and ₹272 (8 × 34) survive; ½ is the smallest fraction, so the first share is ₹204.
Common trap. "₹272" — also a multiple of ₹34, but it is the ⅔ person's 8 parts; the ½ person gets the smallest share, 6 parts.