Question
The monthly incomes of A, B and C are in the ratio 5 : 7
: 9. Their monthly savings are in the ratio 2 : 3 : 4. The ratio of A’s expenditure to C’s expenditure is 3 : 5. If the total monthly income of A, B and C is Rs. 42,000, find: (i) B’s monthly savings (ii) The difference between the monthly expenditures of C and A. Choose the Correct Options - A) (i) Rs. 6,000 (ii) Rs. 4,000. B) (i) Rs. 1,000 (ii) Rs. 2,000. C) (i) Rs. 6,700 (ii) Rs. 4,200. D) (i) Rs. 2,250 (ii) Rs. 4,000. E) None of theseSolution
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.
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