Given:

Incomes ratio of Peter and Paul = 4:3 Expenses ratio of Peter and Paul = 3:2 Both save Rs. 6,000 at the end of the month

Let: Peter's income = $4x$ Paul's income = $3x$ Peter's expense = $3y$ Paul's expense = $2y$

Savings Equation: Peter's savings = Income - Expense → $4x - 3y = 6,000$ Paul's savings = Income - Expense → $3x - 2y = 6,000$

Solve the system of equations: $4x - 3y = 6,000$ $3x - 2y = 6,000$

Multiply the second equation by 4 and the first equation by 3: $(3x - 2y) \times 4$ → $12x - 8y = 24,000$ $(4x - 3y) \times 3$ → $12x - 9y = 18,000$

Subtract the second equation from the first: $(12x - 8y) - (12x - 9y) = 24,000 - 18,000$ $y = 6,000$

Substitute y = 6,000 in the first equation: $4x - 3(6,000) = 6,000$ $4x - 18,000 = 6,000$ $4x = 24,000$ $x = 6,000$

Incomes: Peter's income = $4x = 4 \times 6,000 =$ Rs. 24,000 Paul's income = $3x = 3 \times 6,000 =$ Rs. 18,000

Answer: Peter's income = Rs. 24,000 Paul's income = Rs. 18,000 Correct Option: A. Rs. 24,000 and Rs. 18,000