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?

Question

The monthly salary for a person who follows the same expense pattern, but has a petrol expense of Rs 500 p.m., is:

Answer 1

Rather than compute both years' headcounts and subtract, split each department's change into two parts: the change that comes purely from the company growing by 2,000 employees, and the change that comes from the department's own share shifting. Using new% for the 2006 share and old% for the 2005 share, and old total = 18,000:

\[ \Delta = (\text{new\%} \times 2000) + (\text{new\%} - \text{old\%}) \times 18000 \]

A (Administration): $(0.24 \times 2000) + (0.24-0.22)\times 18000 = 480 + 360 = 840$.
B (Operations): $(0.26 \times 2000) + (0.26-0.23)\times 18000 = 520 + 540 = 1060$.
D (Finance & Accounts): $(0.20 \times 2000) + (0.20-0.29)\times 18000 = 400 - 1620 = -1220$, an absolute change of 1220. The department's share actually dropped by 9 percentage points, which pulls its headcount down hard even though the company as a whole grew.
E (Corporate HQ): $(0.10 \times 2000) + (0.10-0.08)\times 18000 = 200 + 360 = 560$.

The magnitudes are 840, 1060, 1220 and 560. Finance & Accounts shows the biggest swing because it lost 9 percentage points of the company's headcount while the company itself was expanding, so both effects push in the same direction and add up.

Let's summarize:

A department's absolute headcount change depends on both the overall company growth and its own share change, and the two can reinforce or cancel each other.
D's share fell sharply even as the company grew, giving it the largest net drop.

Finance & Accounts (D) has the maximum absolute change in strength.

Answer 2

Rather than compute both years' headcounts and subtract, split each department's change into two parts: the change that comes purely from the company growing by 2,000 employees, and the change that comes from the department's own share shifting. Using new% for the 2006 share and old% for the 2005 share, and old total = 18,000:

\[ \Delta = (\text{new\%} \times 2000) + (\text{new\%} - \text{old\%}) \times 18000 \]

A (Administration): $(0.24 \times 2000) + (0.24-0.22)\times 18000 = 480 + 360 = 840$.
B (Operations): $(0.26 \times 2000) + (0.26-0.23)\times 18000 = 520 + 540 = 1060$.
D (Finance & Accounts): $(0.20 \times 2000) + (0.20-0.29)\times 18000 = 400 - 1620 = -1220$, an absolute change of 1220. The department's share actually dropped by 9 percentage points, which pulls its headcount down hard even though the company as a whole grew.
E (Corporate HQ): $(0.10 \times 2000) + (0.10-0.08)\times 18000 = 200 + 360 = 560$.

The magnitudes are 840, 1060, 1220 and 560. Finance & Accounts shows the biggest swing because it lost 9 percentage points of the company's headcount while the company itself was expanding, so both effects push in the same direction and add up.

Let's summarize:

A department's absolute headcount change depends on both the overall company growth and its own share change, and the two can reinforce or cancel each other.
D's share fell sharply even as the company grew, giving it the largest net drop.

Finance & Accounts (D) has the maximum absolute change in strength.

Show Hint

The Correct Option is C

Solution and Explanation

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