Shares described through one another — Aptitude Question
Shares described through one another: A sum of ₹3,400 is divided among A, B and C so that A gets ⅔ of what B gets,… Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
A sum of ₹3,400 is divided among A, B and C so that A gets ⅔ of what B gets, and B gets ¼ of what C gets. What is B's share?
Options
- ₹400
- ₹500
- ₹600
- ₹800
Show the answer and the worked solution
Correct answer: C. ₹600
Worked solution
- A = (2/3)B and C = 4B.
- Total = (2/3)B + B + 4B = (17/3)B.
- (17/3)B = 3,400 → B = 3,400 × 3 / 17 = ₹600.
- Check: A = 400, B = 600, C = 2,400, total 3,400. ✓
Answer: ₹600.
The idea
Pick the variable everything else is described against — here B — and write the total in that one variable. Choosing A or C instead makes the fractions much worse.
Shortcut. Clear the fractions with B = 3 units: A = 2 and C = 12, so 17 units = ₹3,400, one unit = ₹200 and B = 3 × 200 = ₹600.
Common trap. "₹400" — working in the 2 : 3 : 12 units and reading off A's 2 units instead of B's 3.