Answer:
A = Rs 48,000
B = Rs 24,000
C = R2 8,000
Step-by-step explanation:
To solve this problem, create and solve a system of linear equations using the given information.
From the given information:
- If the monthly income of A is double than that of B, then A = 2B.
- If the monthly income of B is treble than that of C, then B = 3C.
- If the total income of three persons is Rs 80,000, then A + B + C = 80000.
Therefore, the system of linear equations is:
[tex]\begin{cases}A=2B\\B=3C\\A+B+C=80000\end{cases}[/tex]
Substitute the second equation into the first to create and equation for A in terms of C:
[tex]\begin{aligned}A &= 2B\\&=2(3C)\\&=6C\end{aligned}[/tex]
Substitute this and the second equation into the third equation and solve for C:
[tex]\begin{aligned}A+B+C&=80000\\6C+3C+C&=80000\\10C&=80000\\C&=8000\end{aligned}[/tex]
Now that we have found the monthly income of person C, substitute this value into the expressions for A and B to calculate the monthly incomes of persons A and B:
[tex]\begin{aligned}A &=6C\\&=6(8000)\\&=48000\end{aligned}[/tex]
[tex]\begin{aligned}B &=3C\\&=3(8000)\\&=24000\end{aligned}[/tex]
Therefore, the monthly income of each person is:
- A = Rs 48,000
- B = Rs 24,000
- C = R2 8,000
