Tom and Jerry had pig banks! wow

Let's take the following assumptions to simplify the problem:

Tom's savings=x and Tom's total income=X

Jerry's expenditure=y and Jerry's total income=Y

Now according to the problem, Tom saves 10% more than his expenditure. Mathematically, $(X-x)+(X-x) \times 10 \text{\%}=y \Rightarrow \dfrac{(X-x)11}{10}=x \Rightarrow X=\dfrac{21x}{11}$ ---(1)

And Jerry spends 10% more than his savings. So mathematically,

$(Y-y)+(Y-y) \times 10 \text{\%}=y \Rightarrow \dfrac{(Y-y)11}{10}=y \Rightarrow Y=\dfrac{21y}{11}$ ---(2)

And also given that Tom's savings is 10% more than Jerry's expenditure. So,

$y+y \times 10 \text{\%}=x \Rightarrow \dfrac{11y}{10}=x \Rightarrow \dfrac xy=\dfrac{11}{10}$ ---(3)

Now lets enter into the simplifying part $:-$

Dividing (1) by (2) we get

$\dfrac XY=\dfrac{ \left( \dfrac{21x}{11} \right) }{\left( \dfrac{21y}{11} \right) }=\dfrac{x}{y}$

From the equation (3), we can substitute the value of $\dfrac xy$ into the above equation and we will get

$\dfrac XY=\dfrac{11}{10}$

Hence the ratio of the total incomes of Tom and Jerry is $11:10 .\square$

enjoy!