Answer:
[tex] \sf \: \fbox{Option C) \: The salary of B is 6000₹}[/tex]
Step-by-step explanation:
Let the salary or A is x and salary of B is y.
now,
Condition one,The sum of 3/4th of A’s salary and 5/3rd of B’s salary is ₹16,000.
writing above statement in equation form,
[tex] \sf \frac{3x}{4} + \frac{5y}{3} = 16000[/tex]
Multiplying above equation with twelve,
[tex] \sf \frac{3x}{4} + \frac{5y}{3} = 16000 \\ \sf \frac{12 \times 3x}{4} + \frac{12 \times 5y}{3} = 16000 \times 12 \\ \sf \fbox{9x + 20y = 192000} \rightarrow eq. 1[/tex]
and condition two,
The difference of their salaries is ₹2000
[tex] \sf \: x - y = 2000[/tex]
Multiplying above equation with 20
[tex] \sf \fbox{\: 20x -20y = 40000} \rightarrow eq.2[/tex]
On adding equation 1 and equation 2,
[tex] \sf9x + \cancel{20y} = 192000 \\ \sf 20x - \cancel{20y} = 40000 \\ \hline \sf 29x + 0y = 232000 \\ \sf x = \frac{232000}{29} \\ \sf \: \fbox{x = 8000₹}[/tex]
Substituting the value of x in,
[tex] \sf \: x - y = 2000 \\ \sf \: 8000 - y = 2000 \\ \sf \: y = 8000 - 2000 \\ \sf \fbox{y = 6000₹}[/tex]
[tex] \sf \: \fbox{The salary of B is 6000₹}[/tex]
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