The ratio of the incomes of A and B last year was 4 ∶ 3, respectively. The ratios of their individual incomes of the last year and the present year are 3 ∶ 4 and 5 ∶ 6, respectively. If their total income for the present year is Rs. 8.04 lakh, then the income of B last year was∶
Rs. 2.7 lakh
Step 1 — Last year's incomes:
Let A and B's last-year incomes be \(4x\) and \(3x\) (lakh).
Step 2 — Present-year incomes:
A's last : present = 3 : 4, so A now earns \(4x \times \tfrac{4}{3} = \tfrac{16x}{3}\). B's last : present = 5 : 6, so B now earns \(3x \times \tfrac{6}{5} = \tfrac{18x}{5}\).
Step 3 — Use the total:
\[\frac{16x}{3} + \frac{18x}{5} = 8.04 \implies \frac{134x}{15} = 8.04\]
\[x = \frac{8.04 \times 15}{134} = 0.9\]
Therefore B's income last year \(= 3x = \mathbf{Rs.\ 2.7\ lakh}\).
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