Single correct option
The monthly incomes of A and B are in the ratio 5 : 4 and their monthly expenditures are in the ratio 3 : 2. If each of them saves ₹4,000 a month, what is A's monthly income?
- A. ₹10,000
- B. ₹12,000
- C. ₹15,000
- D. ₹8,000
Show answer and solution
Answer: (A) ₹10,000
Let incomes be 5x and 4x and expenditures 3y and 2y.
Savings: 5x − 3y = 4000 and 4x − 2y = 4000.
From the second, 2x − y = 2000, so y = 2x − 2000. Substituting: 5x − 6x + 6000 = 4000 ⇒ x = 2000.
A's income = 5x = ₹10,000 (expenditure 6,000, saving 4,000; B: income 8,000, expenditure 4,000, saving 4,000 ✓).
Tip: Check options quickly — for A = 10,000, B = 8,000; expenditures 6,000 and 4,000 are in ratio 3 : 2. ✓
Savings: 5x − 3y = 4000 and 4x − 2y = 4000.
From the second, 2x − y = 2000, so y = 2x − 2000. Substituting: 5x − 6x + 6000 = 4000 ⇒ x = 2000.
A's income = 5x = ₹10,000 (expenditure 6,000, saving 4,000; B: income 8,000, expenditure 4,000, saving 4,000 ✓).
Tip: Check options quickly — for A = 10,000, B = 8,000; expenditures 6,000 and 4,000 are in ratio 3 : 2. ✓
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