Workforce and wage adjustment in a firm: the number of employees reduces in the ratio 3:2, while the average wage per employee increases in the ratio 20:27. Compute the overall percentage saving or gain on the total wage bill compared to the previous wage outlay, and state the net effect clearly.

Introduction:
Questions that combine changes in staff count and per-employee wages test the idea of multiplicative effects. Instead of averaging the given percentages or ratios, you must compare the total wage bill before and after the change to determine the overall saving or increase.

Given Data / Assumptions:

• Headcount reduces from 3 parts to 2 parts (employee ratio 3:2).
• Average wage per employee increases from 20 parts to 27 parts (wage ratio 20:27).
• Total wage bill = number of employees * average wage per employee.

Concept / Approach:
Compute an index for the old and new wage bills using the product of the two ratios. Old bill is proportional to 3 * 20. New bill is proportional to 2 * 27. Compare these to find the net change as a percentage of the old bill.

Step-by-Step Solution:
Old wage bill index = 3 * 20 = 60New wage bill index = 2 * 27 = 54Absolute change = 60 - 54 = 6 (a reduction)Percentage change relative to old = 6 / 60 * 100 = 10%

Verification / Alternative check:
Scale to concrete numbers. Suppose initially there are 300 employees paid Rs 20 each: total = 6000. After change, employees = 200 and wage = Rs 27 each: total = 5400. Reduction = 600, which is 10% of 6000. This confirms the result.

Why Other Options Are Wrong:

• 9.09%: arises from using the new wage bill as base instead of the old bill.
• 11.11%: comes from reversing the headcount ratio or misapplying percentages.
• None of these: incorrect because 10% is correct.

Common Pitfalls:

• Averaging the ratios or converting them to percentages before combining.
• Basing the percentage reduction on the new bill rather than the old baseline.

Final Answer:
10% reduction (a 10% saving on the previous wage bill)