The ratio of earnings to expenditure of X is 5 : 3 and that of Y is 7 : 6. If the savings of X is double the that of Y, then what could be the ratio of total earnings of X and Y together to the total expenditure of X and Y together?
Solution
Let the earnings of X be $5x$, then the expenditure of X will be $3x$.
$\therefore $ savings of X $=5x-3x=2x$
Let the earnings of Y be $7y$, then the expenditure of Y will be $6y$.
$\therefore $ savings of Y $=7y-6y=y$
Given savings of X are double that of Y
$\therefore \dfrac{2x}{y}=2 \Rightarrow x=y$
$\therefore $ the ratio of total earnings of X and Y to the total expenditure of X and Y
$=\dfrac{5x+7y}{3x+6y}=\dfrac{5x+7x}{3x+6x}=\dfrac{12}{9}=4:3$