Question

The pie-charts below give the percentage distribution of employees in different Departments in XYZ Company Ltd. during the years 2005 and 2006. A - Administration; B - Operations; C - Sales & Marketing; D - Finance & Accounts; E - Corporate HQ.

2005 (total employees 18,000): A 22%, B 23%, C 18%, D 29%, E 8%.

2006 (total employees 20,000): A 24%, B 26%, C 20%, D 20%, E 10%.

In which department is the variation in strength (absolute change) the maximum in 2006 compared to 2005?

• A. A (Administration)
• B. B (Operations)
• C. D (Finance & Accounts)
• D. E (Corporate HQ)

Hint:

Convert every department's percentage share into an actual headcount for 2005 and 2006 using that year's own total, then take the absolute difference for each department and compare, remembering a department can drop even while the company grows.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
"Variation in strength" here means the absolute change in headcount, not the percentage-point change, so every department's actual employee count must be worked out for both years.

Step 2: Key Formula or Approach:
Headcount \( = \) percentage share \( \times \) total employees for that year; absolute change \( = |\text{2006 headcount} - \text{2005 headcount}| \).

Step 3: Detailed Explanation.
A (Administration): \( 22\% \times 18{,}000 = 3{,}960 \to 24\% \times 20{,}000 = 4{,}800 \), change \( = 840 \).
B (Operations): \( 23\% \times 18{,}000 = 4{,}140 \to 26\% \times 20{,}000 = 5{,}200 \), change \( = 1{,}060 \).
C (Sales & Marketing, not an option but shown for completeness): \( 18\% \times 18{,}000 = 3{,}240 \to 20\% \times 20{,}000 = 4{,}000 \), change \( = 760 \).
D (Finance & Accounts): \( 29\% \times 18{,}000 = 5{,}220 \to 20\% \times 20{,}000 = 4{,}000 \), change \( = -1{,}220 \), so \( |{-1220}| = 1{,}220 \).
E (Corporate HQ): \( 8\% \times 18{,}000 = 1{,}440 \to 10\% \times 20{,}000 = 2{,}000 \), change \( = 560 \).

Step 4: Final Answer:
Comparing 840, 1,060, 1,220 and 560, department D has the largest absolute change at 1,220 employees, even though its percentage share actually fell.
\[ \boxed{\text{D (Finance \& Accounts)}} \]