We are given the following details:

• One year ago, the ratio of income between A and B was $3 : 5$.
• The ratio of last year’s income (LYI) to current year's income (CYI) is:
  • For A: $2 : 3$
  • For B: $4 : 5$
• The total current income (CYI) of A and B combined is $Rs. 4300$.

Step 1: Let’s assume their last year's incomes

Let:

• A’s last year income (LYI) = $3x$
• B’s last year income (LYI) = $5x$

Step 2: Express current incomes using ratios

Using the given ratios of LYI to CYI:

• For A: LYI to CYI is $2 : 3$, meaning current income of A is $\frac{3}{2}$ times their LYI: $A's \ CYI = \frac{3}{2} \times 3x = \frac{9x}{2}$
• For B: LYI to CYI is $4 : 5$, meaning current income of B is $\frac{5}{4}$ times their LYI: $B's \ CYI = \frac{5}{4} \times 5x = \frac{25x}{4}$

Step 3: Sum of current incomes

The total current income of A and B is given as Rs. 4300, so: $\frac{9x}{2} + \frac{25x}{4} = 4300$

Step 4: Solve the equation

To simplify, find a common denominator: $\frac{18x}{4} + \frac{25x}{4} = 4300$ $\frac{43x}{4} = 4300$ Multiply both sides by 4: $43x = 17200$ Solve for $x$: $x = \frac{17200}{43} = 400$

Step 5: Find individual current incomes

• A’s CYI = $\frac{9x}{2} = \frac{9 \times 400}{2} = 1800$
• B’s CYI = $\frac{25x}{4} = \frac{25 \times 400}{4} = 2500$

Final Answer:

• A's current income is Rs. 1800.
• B's current income is Rs. 2500.

Let me know if you need more details!

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Here are 5 related questions to expand on this:

1. What would happen if A and B's income ratio last year was reversed?
2. How would the calculation change if the total income was different?
3. What if only one person’s income increased, how would we calculate that?
4. Can we determine the percentage increase in their incomes from last year?
5. How would this problem change if their current total income was given as a ratio?

Tip: When solving ratio problems, it's useful to convert ratios into algebraic expressions to simplify calculations.