Technicians and the rest — Averages Aptitude Question
Technicians and the rest: The average salary of all workers in a workshop is ₹8,000. The average of 7 technicians… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
The average salary of all workers in a workshop is ₹8,000. The average of 7 technicians is ₹12,000 and of the remaining workers ₹6,000. How many workers are there in all?
Options
- 18
- 20
- 21
- 24
Show the answer and the worked solution
Correct answer: C. 21
Worked solution
- 84,000 + 6,000(n − 7) = 8,000n.
- 84,000 + 6,000n − 42,000 = 8,000n → 42,000 = 2,000n.
- n = 21.
- Check: 7 × 12,000 + 14 × 6,000 = 84,000 + 84,000 = 1,68,000 = 21 × 8,000. ✓
Answer: 21.
The idea
Set the sum of the group totals equal to the overall total and solve for the unknown count. Alligation gives the same answer faster: the ratio of technicians to others is (8,000 − 6,000) : (12,000 − 8,000) = 1 : 2.
Shortcut. Balance the surplus: 7 technicians are ₹4,000 above ₹8,000 (₹28,000 in all) and each other worker is ₹2,000 below, so 14 others are needed — 21 in all.
Common trap. "20" — a round total that nearly balances: 7 technicians and 13 others average (84,000 + 78,000) ÷ 20 = ₹8,100, just above ₹8,000.