If the number of employees in IT and Marketing departments increases by 60%…
2024
If the number of employees in IT and Marketing departments increases by 60% and 20% respectively in the next year, then what will be the ratio of the number of employees in the IT and Marketing departments in the next year?
Answer: C. 16 : 21 — Concept: percentage growth and ratios When a quantity grows by p%, its new value equals the old value multiplied by the growth factor (1 + p/100). A ratio…
- A.
13 : 19
- B.
3 : 4
- C.
16 : 21
- D.
2 : 3
Show answer & explanation
Correct answer: C
Concept: percentage growth and ratios
When a quantity grows by p%, its new value equals the old value multiplied by the growth factor (1 + p/100). A ratio only compares two quantities, so when both quantities are given as percentages of one common total, that common total cancels out of the comparison. The new ratio is therefore (first share × its growth factor) : (second share × its growth factor), and the actual head counts are never required.
Application to this table
From the table, IT accounts for 8% of the workforce and Marketing for 14%, so this year IT : Marketing = 8 : 14.
IT grows by 60%, so its growth factor is 1 + 60/100 = 1.6; Marketing grows by 20%, so its growth factor is 1 + 20/100 = 1.2.
Next year, IT : Marketing = (8 × 1.6) : (14 × 1.2) = 12.8 : 16.8.
Multiply both terms by 10 to clear the decimals: 128 : 168.
Divide both terms by their HCF, 8, to reach lowest terms: 16 : 21.
Cross-check with actual head counts
The Marketing department has 560 employees and that is 14% of the workforce, so the total workforce is 560 × 100/14 = 4000 and the IT department has 8% of 4000 = 320 employees.
Department | This year | Growth factor | Next year |
|---|---|---|---|
IT | 320 | 1.6 | 512 |
Marketing | 560 | 1.2 | 672 |
Dividing both next-year counts by their HCF, 32, gives 512 : 672 = 16 : 21 — the same answer reached without the head counts. As a decimal, 16/21 ≈ 0.762, which matches 12.8/16.8 ≈ 0.762.
Common slips to avoid
Adding percentage points instead of scaling — using 8 + 60 and 14 + 20 — treats a 60% increase as 60 percentage points and answers a different question.
Swapping the two growth factors, applying 1.6 to Marketing and 1.2 to IT, reverses which department grows faster.
Comparing the unchanged shares 8 : 14 = 4 : 7 gives this year's ratio, not next year's.
Result
The ratio of employees in the IT and Marketing departments next year is 16 : 21.