A company, during a period of inflation, reduced its staff in the ratio 5 : 3 and increased the average salary per employee in the ratio 7 : 8. By doing this, the company saved Rs. 55,000 in total monthly expenditure. What was the initial total expenditure of the company?

Introduction / Context:
This question mixes ratios with percentage style changes in a company's total expenditure on salaries. The staff strength is reduced, while the average salary per employee is increased. The result is a net reduction in total salary expenditure, which is given. We are asked to find the initial total expenditure. This is a typical application of multiplying ratios and comparing original and new totals in quantitative aptitude.

Given Data / Assumptions:

• Staff is reduced in the ratio 5 : 3, meaning new staff = 3/5 of initial staff.
• Average salary per employee is increased in the ratio 7 : 8, meaning new average salary = 8/7 of the initial average salary.
• Due to these changes, the company saves Rs. 55,000 in total expenditure.
• We assume salary changes apply uniformly to all remaining employees.

Concept / Approach:
Let the original number of employees be N and the original average salary be S. Then the original total salary expenditure E0 = N * S. After the reduction, the number of employees becomes (3/5) * N, and the new average salary becomes (8/7) * S. Hence, new expenditure E1 = (3/5) * N * (8/7) * S. The difference E0 - E1 equals 55,000. Solving this equation in terms of E0 gives the initial total expenditure.

Step-by-Step Solution:
Let original number of employees = N and original average salary = S.Original expenditure E0 = N * S.New number of employees after reduction: N_new = (3 / 5) * N.New average salary after increase: S_new = (8 / 7) * S.New expenditure E1 = N_new * S_new = (3 / 5) * N * (8 / 7) * S.Simplify E1: (3 / 5) * (8 / 7) = 24 / 35, so E1 = (24 / 35) * N * S = (24 / 35) * E0.Given that savings = E0 - E1 = Rs. 55,000.So E0 - (24 / 35) * E0 = 55,000.E0 * (1 - 24 / 35) = 55,000.1 - 24 / 35 = 11 / 35.So (11 / 35) * E0 = 55,000.Therefore, E0 = 55,000 * (35 / 11) = 1,75,000.

Verification / Alternative check:
If original expenditure E0 = Rs. 1,75,000, then new expenditure E1 = (24 / 35) * 1,75,000.Compute E1: 1,75,000 * 24 / 35 = 1,20,000.Savings = E0 - E1 = 1,75,000 - 1,20,000 = 55,000, which matches the given savings.Thus the initial total expenditure is consistent with the information.

Why Other Options Are Wrong:
Other values, such as Rs. 1,55,000 or Rs. 1,60,000, do not produce a saving of Rs. 55,000 when multiplied by the factor 24 / 35. For example, if E0 = 1,60,000, then E1 = (24 / 35) * 1,60,000 = 1,09,714.29 approximately, and the saving would not be exactly Rs. 55,000. Only E0 = 1,75,000 gives the correct saving.

Common Pitfalls:
Some candidates confuse the direction of the ratios and incorrectly take new staff as 5/3 of old staff or new average as 7/8 of old average. Others subtract the ratios directly instead of using them as multiplicative factors. Always write original and new quantities explicitly, convert percentage like changes into multiplicative ratios, and then compare the products for expenditure.

Final Answer:
The initial total expenditure of the company was Rs. 1,75,000.