A's income is to B's income as 5 : 7. A saves Rs. 4,000 and B saves Rs. 5,000. If A's spending is two-thirds of B's spending, wha…

Question

A's income is to B's income as 5 : 7. A saves Rs. 4,000 and B saves Rs. 5,000. If A's spending is two-thirds of B's spending, what is the combined income of A and B?

1. A. Rs. 22,200/-
2. B. Rs. 24,000/- (Correct answer)
3. C. Rs. 22,800/-
4. D. Rs. 46,800/-

Correct Answer

Option B — Rs. 24,000/-

Detailed Solution & Explanation

The correct answer is Rs. 24,000/-.

Key Points

• A:B income=5:7. A spends = 5k−4000, B spends = 7k−5000.
• A's spending = (2/3)B's: 3(5k−4000)=2(7k−5000) → k=2000.
• Combined income = 5(2000)+7(2000) = 24000.

Additional Information

• The governing identity is Income − Expenditure = Savings, so expenditure is written as income minus savings before any ratio is applied.
• Taking incomes as 5k and 7k: A spends 5k − 4,000 and B spends 7k − 5,000. The condition *A's spending is two-thirds of B's* gives 3(5k − 4,000) = 2(7k − 5,000), so 15k − 12,000 = 14k − 10,000 and k = 2,000.
• Incomes are therefore ₹10,000 and ₹14,000, a combined ₹24,000; spending is ₹6,000 and ₹9,000, which is indeed in the ratio 2 : 3.
• Always substitute the value of k back and confirm the stated condition — it catches sign slips, which are the usual source of error in this question type.