The ratio of the incomes of A and B in 2020 was 5 : 4. The ratios of their individual income in 2020 and 2021 were 4 : 5 and 2 : 3, respectively. If the total income of A and B in 2021 was Rs. 7,05,600, then what was the income (in Rs.) of B in 2021?

Solution(By Examveda Team)

\[\begin{array}{*{20}{c}} {}&{{\text{Last year}}}&{{\text{Current year}}} \\ {{\text{A}} \to }&{{4_{ \times 1 \times 5}} = 20}&{{5_{ \times 1 \times 5}} = 25} \\ {{\text{B}} \to }&{{2_{ \times 2 \times 4}} = 16}&{{3_{ \times 2 \times 4}} = 24} \end{array}\]
Ratio of final year income of A and B. So because we taken income 20, 16
Ratio of present age of both = 25 : 24
Sum of present age of both = 25 + 24 = 49 units
49 units → 705600
1 unit → 14400
24 units → 14400 × 24 = 345600
B's income is 2021 = 345600

Alternate solution
\[\begin{array}{*{20}{c}} {}&{\text{A}}&:&{\text{B}} \\ {{\text{Previous year}} \to }&{5x}&:&{4x} \end{array}\]
A's present income : final year and present year = 4 : 5
4 units = 5x
5 units = 5x × $$\frac{5}{4}$$ = $$\frac{{25}}{4}$$x
B's present income : final year and present year = 2 : 3
2 units = 4x
3 units = 3x × $$\frac{4}{2}$$ = 6x
\[\begin{array}{*{20}{c}} {}&{\text{A}}&:&{\text{B}} \\ {{\text{Present year}} \to }&{\frac{{25}}{4}x}&:&{6x} \end{array}\]
$$\frac{{25}}{4}$$x + 6x = $$\frac{{49}}{4}$$x → 705600
x = 14400 × 4 = 57600
B's income = 6x = 6 × 57600 = 345600
B's income in 2021 = 345600