Last year the incomes of A and B were in the ratio 4 : 3. The ratios of their last year’s income to this year’s income are 5 : 6 for A and 3 : 4 for B. If their total income this year is Rs 4,400, find their incomes this year.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A: Rs 2,400, B: Rs 2,000
Write last year’s incomes with one multiplier, then scale each by its own last-year : this-year ratio.
Last year: A \(=4k\), B \(=3k\)
This year A \(\displaystyle =4k\times\frac{6}{5}=4.8k\)
This year B \(\displaystyle =3k\times\frac{4}{3}=4k\)
\(4.8k+4k=8.8k=4400\), so \(k=500\)
A \(=4.8\times500=\) Rs 2,400; B \(=4\times500=\) Rs 2,000
This year A earns Rs 2,400 and B earns Rs 2,000.