Employee counts and wages ratio: In a factory, employees of types A, B, and C are in the ratio 9 : 13 : 18, with 54 employees of type C. Their per-employee wages are in the ratio 10 : 7 : 4. If each type-B employee earns ₹ 1400, find the total wages paid to all type-A employees.

Introduction / Context:
When counts and per-head wages follow separate ratios, the total payout to a category is the product of the number of employees in that category and the per-head wage. Known values allow solving the common wage factor and thus the required total.

Given Data / Assumptions:

• Counts A : B : C = 9 : 13 : 18; C count = 54 ⇒ scaling factor = 3.
• Per-head wages A : B : C = 10 : 7 : 4.
• Per-head wage for B = ₹ 1400.

Concept / Approach:
From counts, A = 9*3 = 27 employees, B = 13*3 = 39 employees. From per-head wages, if B is 7k = 1400, then k = 200 and A per-head = 10k = ₹ 2000. Multiply by A’s count to get total A wages.

Step-by-Step Solution:
k = 1400 / 7 = 200.A per-head wage = 10k = ₹ 2000.A employees = 9*3 = 27.Total A wages = 27 * 2000 = ₹ 54000.

Verification / Alternative check:
C’s per-head wage would be 4k = ₹ 800; B has 39 employees at ₹ 1400, confirming k = 200 is consistent across categories.

Why Other Options Are Wrong:

• ₹ 51000, ₹ 56000, ₹ 59000 arise from miscounting A employees or miscomputing per-head wage from the ratio.

Common Pitfalls:

• Using the count ratio as the wage ratio or vice versa.
• Forgetting to scale counts using the given C count.

Final Answer:
₹ 54000