UPSC Prelims 2002 Q68: Science & Technology – Quantitative Aptitude
In a company 60 % of the employees are men. Of these, 40 % are drawing more than Rs
50,000 per year. If 36 % of the total employees of the company draw more than Rs 50,000 per
year, what is the percentage among women who are drawing less than Rs 50,000 per year?
- (a) 70
- (b) 60
- (c) 40
- (d) 30
Answer: (a) 70
Explanation
Women employees drawing less than Rs 50,000 per year
| Quantity (as % of all employees) | Value |
|---|---|
| Men | 60% |
| Men drawing more than Rs 50,000 | 40% of 60% = 24% |
| All drawing more than Rs 50,000 | 36%, so women drawing more = 36 − 24 = 12% |
| Women | 100 − 60 = 40% |
Women are 40 per cent of the employees, and 12 per cent of all employees are women drawing more than Rs 50,000. So the share of women drawing more is 12/40 = 30 per cent, and the share of women drawing less than Rs 50,000 is 70 per cent.
Answer: (a) 70.
Why each option is right or wrong
- (a) CORRECT. 100 − 30 = 70 per cent of women draw less.
- (b) Incorrect. 60 per cent would mean only 16 per cent of the total in the higher bracket for women.
- (c) Incorrect. 40 per cent is the share of women in the company.
- (d) Incorrect. 30 per cent is the share of women drawing more than Rs 50,000.
Key point
Convert every figure to a percentage of the total, then divide by the group size.
Remember
Among 40 women, 12 earn more, so 28 earn less: 70%.
Common mistakes
- Giving 30%, the share drawing more, not less.
- Taking 36% − 40% of men directly without scaling.
- Dividing 12% by 100 instead of by the 40% share of women.
Exam tip
Use 100 employees: 60 men, 24 rich men, 36 rich total, 12 rich women out of 40.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Percentage)