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Income of $\text{A}$ and $\text{B}$ are in the ratio $4:7$ and their spending is in the ratio $6:11.$ If $\text{A}$ saves one third of his income, then the ratio of their savings will be :

1. $12:19$
2. $11:19$
3. $3:5$
4. $10:19$

lets assume that $A,B$ incomes are $4x,7x$ and their expenditures are in the ratio of $6x,11x$

Note: saving =total income-expenditure

now according to the given information:

$4x-6y=\frac{4x}{3}$

$\implies 4x=9y \implies x=\frac{9y}{4}$

so required saving ratio=$\frac{4x-6y}{7x-11y}$

put x value in given ration we get:

$\implies \frac{\frac{36y}{4}-6y}{\frac{63y}{4}-11y}$

$\implies \frac{3y}{19y/4}=\frac{12}{19}=12:19$

Option (A) is correct.
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