Question : The income of A is $\frac{2}{3}$ of B's income and the expenditure of A is $\frac{3}{4}$ of B's expenditure. If $\frac{1}{3}$ of the income of B is equal to the expenditure of A, then the ratio of the savings of A to those of B is:
Option 1: 5 : 3
Option 2: 3 : 5
Option 3: 4 : 3
Option 4: 3 : 4
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Correct Answer: 3 : 5
Solution :
Income of A = $\frac{2}{3}$ of B's income
Let the income of A = $2x$ and income of B = $3x$
Expenditure of A = $\frac{3}{4}$ of B's expenditure
Let expenditure of A = $3y$ and expenditure of B = $4y$
$\frac{1}{3}$ of B's income = Expenditure of A
So, $\frac{3x}{3} = 3y$
⇒ $x= 3y$
Ratio of savings = $(2x-3y) : (3x-4y)= (6y-3y) : (9y-4y) = 3y:5y = 3: 5$
Hence, the correct answer is 3 : 5.
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