Last year the incomes of A and B were in the ratio 3 : 5. The ratios of their last year’s income to this year’s income are 2 : 3 for A and 4 : 5 for B. If their total income this year is Rs 4,300, find their incomes this year.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A: Rs 1,800, B: Rs 2,500
Write last year’s incomes with one multiplier, then scale each by its own last-year : this-year ratio.
Last year: A \(=3k\), B \(=5k\)
This year A \(\displaystyle =3k\times\frac{3}{2}=4.5k\)
This year B \(\displaystyle =5k\times\frac{5}{4}=6.25k\)
\(4.5k+6.25k=10.75k=4300\), so \(k=400\)
A \(=4.5\times400=\) Rs 1,800; B \(=6.25\times400=\) Rs 2,500
This year A earns Rs 1,800 and B earns Rs 2,500.