The monthly incomes of A and B are in the ratio 7 : 5 and their expenditures are in the ratio 3 : 2. If each saves ₹ 1500 per month, find their monthly incomes.

Let monthly income of A be 7x and B be 5x.

Let monthly expenditure of A be 3y and B be 2y.

Given,

Both A and B save ₹ 1500 per month.

For A :

⇒ 7x - 3y = 1500

⇒ 7x = 1500 + 3y

⇒ x = $\dfrac{1500 + 3y}{7}$     …..(1)

For B :

⇒ 5x - 2y = 1500     ……(2)

Substituting value of x from equation (1) in (2), we get :

$\Rightarrow 5x - 2y = 1500 \\[1em] \Rightarrow 5\Big(\dfrac{1500 + 3y}{7}\Big) - 2y = 1500 \\[1em] \Rightarrow \Big(\dfrac{7500 + 15y}{7}\Big) - 2y = 1500 \\[1em] \Rightarrow \Big(\dfrac{7500 + 15y - 14y}{7}\Big) = 1500 \\[1em] \Rightarrow 7500 + y = 10500 \\[1em] \Rightarrow y = 10500 - 7500 \\[1em] \Rightarrow y = 3000.$

Substituting value of y in equation (1), we get :

$\Rightarrow x = \dfrac{1500 + 3y}{7} \\[1em] \Rightarrow x = \dfrac{1500 + 3 \times 3000}{7} \\[1em] \Rightarrow x = \dfrac{1500 + 9000}{7} \\[1em] \Rightarrow x = \dfrac{10500}{7} = 1500.$

A's income = ₹ 7x = ₹ 7 × 1500 = ₹ 10,500,

B's income = ₹ 5x = ₹ 5 × 1500 = ₹ 7,500.

Hence, A's income = ₹ 10,500, B's income = ₹ 7,500.