Question

b) The monthly income of A is double than that of B and the monthly income of B is treble than that of C. If the total income of three persons is Rs 80,000, find monthly income of each of person. ​

Answer 1

A = Rs 48,000

B = Rs 24,000

C = R2 8,000

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:

`\begin{cases}A=2B\\B=3C\\A+B+C=80000\end{cases}`

Substitute the second equation into the first to create and equation for A in terms of C:

`\begin{aligned}A &= 2B\\&=2(3C)\\&=6C\end{aligned}`

Substitute this and the second equation into the third equation and solve for C:

`\begin{aligned}A+B+C&=80000\\6C+3C+C&=80000\\10C&=80000\\C&=8000\end{aligned}`

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:

`\begin{aligned}A &=6C\\&=6(8000)\\&=48000\end{aligned}`

`\begin{aligned}B &=3C\\&=3(8000)\\&=24000\end{aligned}`

Therefore, the monthly income of each person is:

• A = Rs 48,000
• B = Rs 24,000
• C = R2 8,000