The total number of non-PG female employees in the Production and Marketing…

Concept: when a group's total strength, its share of female employees and its share of post-graduates are all known, a single intersection count fixes the whole two-way classification. The number of post-graduate female employees equals the total number of post-graduates minus the number of post-graduate male employees, and the number of female employees who are not post-graduates equals the total number of female employees minus the post-graduate female employees. A 'what percentage' question is then the required aggregate divided by the stated base, multiplied by 100.

Application to the two departments named in the question:

1. Production: total strength = 3,000; female employees = 20% of 3,000 = 600; post-graduates = 40% of 3,000 = 1,200.

2. Post-graduate female employees in Production = 1,200 - 750 = 450, so non-PG female employees in Production = 600 - 450 = 150.

3. Marketing: total strength = 2,000; female employees = 45% of 2,000 = 900; post-graduates = 60% of 2,000 = 1,200.

4. Post-graduate female employees in Marketing = 1,200 - 900 = 300, so non-PG female employees in Marketing = 900 - 300 = 600.

5. Non-PG female employees in the two departments together = 150 + 600 = 750, and their combined strength = 3,000 + 2,000 = 5,000.

6. Required percentage = (750 / 5,000) x 100 = 15.

Cross-check: filling in all four cells of each department's two-way table must reproduce the strength given in the source table.

Both rows add back to 3,000 and 2,000 exactly, which confirms 750 non-PG female employees out of 5,000 employees, that is 15 per cent.

A common slip is to subtract the post-graduate male employees straight from the number of female employees; the post-graduate total must first be split into male and female before the non-post-graduate female count can be obtained.