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nata0808 [166]
2 years ago
7

{ Question}}" alt=" \large \red{\frak{ Question}}" align="absmiddle" class="latex-formula">
The sum of 3/4th of A’s salary and 5/3rd of B’s salary is ₹16,000. The difference of their salaries is ₹2000. If B’s salary is less than that of A, then what is the salary of B (in ₹)?
(a) 8000 (b) 2000
(c) 6000 (d) 12,000​
\pink{ \dag \: \large\sf{ With \: Explanation }}
​\blue{ \dag \: \large\sf{No Spam }}
Mathematics
1 answer:
lbvjy [14]2 years ago
5 0

Answer:

\sf \:  \fbox{Option C) \: The  salary of B is 6000₹}

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,

\sf \frac{3x}{4}  +  \frac{5y}{3}  =  16000

Multiplying above equation with twelve,

\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

and condition two,

The difference of their salaries is ₹2000

\sf \: x - y = 2000

Multiplying above equation with 20

\sf \fbox{\: 20x -20y = 40000} \rightarrow eq.2

On adding equation 1 and equation 2,

\sf9x +  \cancel{20y} = 192000 \\ \sf 20x - \cancel{20y} = 40000 \\     \hline  \sf 29x  + 0y = 232000 \\  \sf x =  \frac{232000}{29}  \\ \sf \:  \fbox{x = 8000₹}

Substituting the value of x in,

\sf \: x - y = 2000 \\ \sf \: 8000 - y = 2000 \\ \sf \:  y = 8000 - 2000 \\ \sf  \fbox{y = 6000₹}

\sf \:  \fbox{The  salary of B is 6000₹}

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