Question:hard

In an organization, there are four departments A, B, C and D with some accountants, managers, stenographers and office boys working together. Department A has 10 accountants, 8 managers, 7 stenographers and 3 office boys. The total monthly salary of all these employees is Rs. 2,37,500. Department B has 5 stenographers, 12 accountants, 6 managers and 7 office boys. The total monthly salary of all these employees is Rs. 2,31,500. Department C has 4 managers, 4 stenographers, 5 office boys and 7 accountants. The total monthly salary of all these employees is Rs. 1,51,000. If all the respective employees are paid equally in all the departments, then find the total monthly salary of 18 accountants, 11 managers, 10 stenographs and 10 office boys of department D?

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You do not need each individual salary; write the target group as a weighted sum of the three department totals.
Updated On: Jul 21, 2026
  • Rs. 2,85,500
  • Rs. 3,25,500
  • Rs. 3,60,500
  • Rs. 3,85,500
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The Correct Option is D

Solution and Explanation

Step 1: Write the same three department equations.
$ 10x_1+8x_2+7x_3+3x_4=237500 $ (A), $ 12x_1+6x_2+5x_3+7x_4=231500 $ (B), $ 7x_1+4x_2+4x_3+5x_4=151000 $ (C).

Step 2: Look for weights p, q, r pairing accountant and manager first.
Accountant: $ 10p+12q+7r=18 $. Manager: $ 8p+6q+4r=11 $.
Scale the manager equation by $ 7/4 $ to match the r coefficient: $ 14p+10.5q+7r=19.25 $.
Subtracting from the accountant equation: $ -4p+1.5q=-1.25 $.

Step 3: Pair stenographer and office boy equations the same way.
Stenographer: $ 7p+5q+4r=10 $. Office boy: $ 3p+7q+5r=10 $.
Scale the stenographer equation by $ 5/4 $: $ 8.75p+6.25q+5r=12.5 $.
Subtracting from the office boy equation: $ -5.75p+0.75q=-2.5 $.

Step 4: Solve the two reduced equations together.
From $ -4p+1.5q=-1.25 $, $ q = \dfrac{4p-1.25}{1.5} $.
Substituting into $ -5.75p+0.75q=-2.5 $ gives $ p = 0.5 $, then $ q = 0.5 $ and, from any original equation, $ r = 1 $.
This matches the values found by the other elimination order.

Step 5: Apply the weights to the three totals.
$ 0.5 \times 237500 + 0.5 \times 231500 + 1 \times 151000 = 118750+115750+151000=385500 $.

Final Answer:
The required monthly salary total is Rs. 3,85,500. $ Rs. 3,85,500 $
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