Maths · Test of consistency and solution of simultaneous linear equations in two or three variables using matrices
The total salary drawn by 3 watchmen, A, B and C is Rs. 1720. They spend 70\%, a
The total salary drawn by 3 watchmen, A, B and C is Rs. 1720. They spend 70\%, \( 60 \% \) and \( 50 \% \) respectively from their salaries. If the balance with them are into Ratio \( 1: 2: 3, \) what is the salary of each?
- A. A Rs. 300; B Rs. 500; C- Rs. 700
- B. A Rs. 200; B Rs. 300; C-Rs. 650
- C. A Rs. 100; B Rs. 300; C-Rs. 600
- D. A Rs. 400; B Rs. 600; C- Rs. 720
Step-by-step solution
Let salaries be a, b, c. Then a+b+c=1720. Balances: 0.3a, 0.4b, 0.5c in ratio 1:2:3. So 0.3a = k, 0.4b = 2k, 0.5c = 3k => a = 10k/3, b = 5k, c = 6k. Sum = (10/3+5+6)k = (43/3)k = 1720 => k=120. Thus a=400, b=600, c=720.
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