The ratio of the income of A and B in the last year was 4 : 3. The ratios of their individual incomes in the last year and the present year are 3 : 4 and 5 : 6, respectively. If their total income in the present year in Rs. 24.12 lakhs, then the sum of the income (in Rs. lakh) of A in the last year and that of B in the present year is:

Answer: Option C

\begin{array}{*{20}{c}} {}&{{\text{Last year}}}&{{\text{Current year}}} \\ {{\text{A}} \to }&{{3_{ \times 5 \times 4}} = 60}&{{4_{ \times 5 \times 4}} = 80} \\ {{\text{B}} \to }&{{5_{ \times 3 \times 3}} = 45}&{{6_{ \times 3 \times 3}} = 54} \end{array}
The ratio of income of A and B in the last year is 4 : 3. So we're making last year's income 60, 45.
Present age ratio of both = 80 : 54
Sum of present age of both = 80 + 54 = 134 units
134 units → 24.12 lakh
1 unit → $$\frac{24.12}{134}$$
Sum of income of A in final year and income of B in present year = 60 + 54 = 114
114 units → $$\frac{24.12}{134}$$ × 114 = 20.52
Sum of income of A in final year and income of B in present year = 20.52 lakh

Alternate solution
\begin{array}{*{20}{c}} {}&{\text{A}}&{\text{B}} \\ {{\text{Previous year }} \to }&{4x}&{3x} \end{array}
A's present salary : Ratio of final year to present year = 3 : 4
3 units = 4x
4 units $$=4x\times \frac{4}{3}=\frac{16}{3}x$$
B's present salary : Final year and present year = 5 : 6
5 units = 3x
6 units $$=3x\times \frac{6}{5}=\frac{18}{5}x$$
\begin{array}{*{20}{c}} {}&{{\text{A}}\,\,\,}&{{\text{B}}\,\,\,} \\ {{\text{Present year }} \to }&{\frac{{16}}{3}x}&{\frac{{18}}{5}x} \end{array}
$$\begin{array}{rl}& \frac{16}{3}x+\frac{18}{5}x=\frac{134}{15}x\to 24.12\text{ lakh}\\ & x=\frac{24.12\times 15}{134}\end{array}$$
Final year income of A and Present year income of B.
$$\begin{array}{rl}& =4x+\frac{18}{5}x=\frac{38}{5}x\\ & \frac{38}{5}x\to \frac{24.12\times 15}{134}\times \frac{38}{5}=20.52\end{array}$$
Final year income of A and Present year income of B = 20.52 lakh