In a factory, the number of employees decreases in the ratio 8 : 7, while the per-employee salary increases in the ratio 5 : 6. Determine whether the total wage bill increases or decreases, and by what ratio.

Introduction / Context:
When one factor (headcount) decreases and another factor (salary per person) increases, the overall wage bill changes by the product of the individual change factors. We must compute that combined effect.

Given Data / Assumptions:

• Employees change 8 → 7 (multiplier = 7/8).
• Salary per employee changes 5 → 6 (multiplier = 6/5).
• Total wage bill ∝ employees * salary per employee.

Concept / Approach:
Multiply the two multipliers to get the overall change: (7/8) * (6/5). If this product is greater than 1, the total increases; if less than 1, it decreases.

Step-by-Step Solution:
Overall multiplier = (7/8) * (6/5) = 42/40 = 21/20. Since 21/20 > 1, the total wage bill increases. Expressed as a ratio, the increase is 21 : 20 (increased).

Verification / Alternative check:
Try a baseline: 8 workers at ₹5 each → total 40. After change: 7 workers at ₹6 each → total 42. 42 : 40 = 21 : 20 (increased).

Why Other Options Are Wrong:
19 : 20 increased and 20 : 19 decreased reflect incorrect multiplications; 21 : 20 decreased has wrong direction; “None of above” is incorrect because a precise ratio exists.

Common Pitfalls:
Adding ratios instead of multiplying multipliers, or inverting one of the ratios.

Final Answer:
21 : 20 increased