The income of A is 80% of B's income and the expenditure of A is 60% of B's expenditure. If the income of A is equal to 90% of B's expenditure, then by what percentage are the saving of A more than B's savings?

Solution(By Examveda Team)

Income of A is 80% of B
$$\eqalign{ & A = B \times \frac{{80}}{{100}} \cr & \frac{A}{B} = \frac{{4x}}{{5x}} \cr} $$
Expenditure of A is 60% of expenditure of B
$$\eqalign{ & A = B \times \frac{{60}}{{100}} \cr & \frac{A}{B} = \frac{{3y}}{{5y}} \cr} $$
Income of A is 90% of income of B
$$\eqalign{ & 4x = \frac{{90}}{{100}} \times 5y \cr & 8x = 9y \cr & \frac{x}{y} = \frac{9}{8} \cr} $$
Saving ratio of A and B
= (4x - 3y) : (5x - 5y)   [∴ 8x = 9y]
= (4 × 9 - 3 × 8) : (5 × 9 - 5 × 8)
= (36 - 24) : (45 - 40)
= 12 : 5
More = 12 - 5 = 7
More% $$ = \frac{7}{5} \times 100 = 140\% $$

Alternate solution
\[\begin{array}{*{20}{c}} {}&{{\text{A}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{B}}} \\ {{\text{Income}} \to }&{4 \times 5 \times 9 = 180\,\,\,\,\,\,\,\,\,\,5 \times 5 \times 9 = 225} \\ {{\text{Expenditure}} \to }&{3 \times 4 \times 10 = 120\,\,\,\,\,\,\,\,\,\,5 \times 4 \times 10 = 200} \\ {{\text{Saving}} \to }&{\overline {\underline {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,60\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,25\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} } } \end{array}\]
Ratio of A saving to B saving = 60 : 25 = 12 : 5
More = 12 - 5 = 7
More% $$ = \frac{7}{5} \times 100 = 140\% $$