The monthly incomes of A, B and C are in the ratio 5 : 7

Solution

ATQ, Let incomes of A, B, C be 5x, 7x, 9x. Let their savings be 2y, 3y, 4y. Then expenditures are: A: 5x − 2y B: 7x − 3y C: 9x − 4y. Given: (5x − 2y) : (9x − 4y) = 3 : 5 ⇒ (5x − 2y)/(9x − 4y) = 3/5 Cross-multiplying: 5(5x − 2y) = 3(9x − 4y) 25x − 10y = 27x − 12y ⇒ 0 = 2x − 2y ⇒ x = y. Total income: 5x + 7x + 9x = 21x = 42,000 ⇒ x = 2,000. So incomes are: A = 5x = 10,000 B = 7x = 14,000 C = 9x = 18,000. Savings: A = 2x = 4,000 B = 3x = 6,000 C = 4x = 8,000. Expenditures: A = 10,000 − 4,000 = 6,000 B = 14,000 − 6,000 = 8,000 C = 18,000 − 8,000 = 10,000. (i) B’s savings = Rs. 6,000. (ii) Difference (C’s exp − A’s exp) = 10,000 − 6,000 = Rs. 4,000. Answer: (i) Rs. 6,000 (ii) Rs. 4,000.