The income of A is 2/3 of B's income and the expenditure of A is 3/4 of B's expenditure. If 1/3 of the income of B is equal to the expenditure of A, then the ratio of the savings of A to those of B is:

Answer: Option A

Income of A is equal to $$\frac{2}{3}$$ of income of B.
$$\begin{array}{rl}& A=B\times \frac{2}{3}\\ & \frac{A}{B}=\frac{2x}{3x}\end{array}$$
A's expenditure is equal to $$\frac{3}{4}$$ B's expenditure
$$\begin{array}{rl}& A=B\times \frac{3}{4}\\ & \frac{A}{B}=\frac{3y}{4y}\end{array}$$
A's income is equal to $$\frac{1}{3}$$ B's income
3x × $$\frac{1}{3}$$ = 3y
x = 3y
Saving ratio of A and B
= (2x - 3y) : (3x - 4y)   [∵ x = 3y]
= (6y - 3y) : (9y - 4y)
= 3y : 5y
= 3 : 5

Alternate solution
\begin{array}{*{20}{c}} {}&{{\text{A}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{B}}} \\ {{\text{Income}} \to }&{\,\,\,\,\,\,\,{2_{ \times 3 = 6}}\,\,\,{3_{ \times 3 = 9}}} \\ {{\text{Expenditure}} \to }&{3\,\,\,\,\,\,\,\,\,\,\,\,\,\,4} \\ {{\text{Saving}} \to }&{\overline {\underline {\,\,3\,\,\,\,\,:\,\,\,\,\,5\,\,} } } \end{array}