Question

# Ratio of income of $$A$$ and $$B$$ is $$6 : 5$$ ratio of their expenditure is $$3 : 2$$, if $$A$$ saves $$\dfrac {1}{4}^{(th)}$$ of his income , find ratio of their monthly savings?

A
1:2
B
2:3
C
3:4
D
4:5

Solution

## The correct option is C $$3:4$$Let the income of $$A=6x$$Let the income of $$B=5x$$Let the expenditure of $$A=3y$$Let the expenditure of $$B=2y$$Therefore , savings of $$A=6x-3y$$Savings of $$B=5x-2y$$Now, as $$A$$ saves $$\cfrac{1}{4}^{th}$$ of his income,$$6x-3y=\cfrac{1}{4}(6x)$$$$24x-12y=6x$$$$18x=12y$$$$3x=2y$$Now, ratio of savings of $$A$$ and $$B$$ $$=\cfrac{6x-3y}{5x-2y}$$$$=\cfrac{6x-\left(\cfrac{3}{2}x\right)\times 3}{5x-3x}=\cfrac{3}{4}=3:4$$Maths

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