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:

Solution(By Examveda Team)

\[\begin{array}{*{20}{c}} {}&{{\text{Last year}}}&{{\text{Current year}}} \\ {{\text{A}} \to }&{{3_{ \times 5 \times 4}} = 60}&{{4_{ \times 5 \times 4}} = 80} \\ {{\text{B}} \to }&{{5_{ \times 3 \times 3}} = 45}&{{6_{ \times 3 \times 3}} = 54} \end{array}\]
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 $$ = 3x \times \frac{6}{5} = \frac{{18}}{5}x$$
\[\begin{array}{*{20}{c}} {}&{{\text{A}}\,\,\,}&{{\text{B}}\,\,\,} \\ {{\text{Present year }} \to }&{\frac{{16}}{3}x}&{\frac{{18}}{5}x} \end{array}\]
$$\eqalign{ & \frac{{16}}{3}x + \frac{{18}}{5}x = \frac{{134}}{{15}}x \to 24.12{\text{ lakh}} \cr & x = \frac{{24.12 \times 15}}{{134}} \cr} $$
Final year income of A and Present year income of B.
$$\eqalign{ & = 4x + \frac{{18}}{5}x = \frac{{38}}{5}x \cr & \frac{{38}}{5}x \to \frac{{24.12 \times 15}}{{134}} \times \frac{{38}}{5} = 20.52 \cr} $$
Final year income of A and Present year income of B = 20.52 lakh