Incomes of $A$ and $B$ are in the ratio $4:5$ and expenditures are in the ratio $5:6$ If incomes of $A$ and $B$ are in the ratio $4:5$ and expenditures are in the ratio $5:6$, whatever be the absolute value of their incomes and expenditure $B$ will save more. How?
 A: Express it in the form of equations. Say A's income is $i_A$ and A's expenditure is $e_A$. 
Then by the ratios above B's income is $i_B=\frac{5}{4}i_A$ and B's expenditure is $e_B=\frac{6}{5}e_A$.
How much will B save is determined by $i_B-e_B=\frac{5}{4}i_A-\frac{6}{5}e_A>\frac{6}{5}i_A-\frac{6}{5}e_A>i_A-e_A$
and the last expression is how much A will save.
A: One way to see it is savings varies linearly with expenditure, and in both extreme cases, B saves more than A, so B saves  more than A under all cases between the extreme cases.
A: Given information:


*

*A makes $x$ and spends $y$

*B makes $\frac54x$ and spends $\frac65y$


Therefore:


*

*A saves $x-y$

*B saves $\frac54x-\frac65y$


Therefore:


*

*B saves $\frac{25}{20}x-\frac{24}{20}y$


Therefore:


*

*B saves $\frac{25}{20}x-\frac{25}{20}y+\frac{1}{20}y$


Therefore:


*

*B saves $\frac{25}{20}(x-y)+\frac{1}{20}y$


Therefore:


*

*B saves $\frac{25}{20}a+\frac{1}{20}y$, where $a$ is A's savings


Keep in mind that $y\geq0$, therefore B saves more than A.
