Two grades of worker — Aptitude Question
Two grades of worker: A firm pays skilled workers ₹800 a day and unskilled workers ₹500 a day. Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A firm pays skilled workers ₹800 a day and unskilled workers ₹500 a day. If the average daily wage is ₹600, what is the ratio of skilled to unskilled workers?
Options
- 1 : 2
- 2 : 1
- 1 : 3
- 3 : 1
Show the answer and the worked solution
Correct answer: A. 1 : 2
Worked solution
- Skilled : unskilled = (600 − 500) : (800 − 600) = 100 : 200 = 1 : 2.
- Check: (1 × 800 + 2 × 500)/3 = 1,800/3 = 600. ✓
Answer: 1 : 2.
The idea
Each group's share is proportional to the other group's distance from the mean. The mean at 600 sits nearer 500, so the cheaper group is larger.
Shortcut. ₹600 is a third of the way from ₹500 to ₹800, so skilled workers are one third of the staff: 1 : 2.
Common trap. "2 : 1" — giving each group its own distance from ₹600 (200 : 100); the nearer wage, ₹500, belongs to the larger group.