Final answer:
To calculate the monthly incomes of A and B, the relations 9x - 4y = Rs 1600 and 7x - 3y = Rs 1600 were solved to find A's income as Rs 3600 and B's as Rs 2800. B is potentially more economical due to a smaller income-to-expense margin, showing financial responsibility.
Step-by-step explanation:
To find the monthly income of A and B, we set up the equations based on the given ratios and savings. Let's denote the monthly income of A as 9x and that of B as 7x. Their monthly expenses then are 4y and 3y, respectively, because their expenses are in the ratio 4:3.
Since both save Rs 1600 per month, their income minus expenditure equals their savings. Therefore, for A: 9x - 4y = 1600, and for B: 7x - 3y = 1600. These two equations need to be solved simultaneously.
Solution:
First, equate the two equations to find a relation between x and y. Subtracting the second equation from the first gives 2x = y. Using this relation in one of the equations, let's say 9x - 4(2x) = 1600, simplifies to x = 400.
Substituting x = 400 into the equations for A's and B's incomes gives us A's monthly income as Rs 3600 (9x) and B's monthly income as Rs 2800 (7x).
Assessing who is more economical involves examining their respective expenditures in relation to their incomes. B, with a smaller income-expense margin, could be viewed as more economical. Through careful budget management and prioritization, they both exhibit a value of financial responsibility.