The incomes of A, B and C are in the ratio 7: | vedclass

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(D) Let the incomes of $A, B$ and $C$ be $₹ 7x, ₹ 9x$ and $₹ 12x$ respectively,and their expenditures be $₹ 8y, ₹ 9y$ and $₹ 15y$ respectively.Given t

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$56: 99: 69$

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(D) Let the incomes of $A, B$ and $C$ be $₹ 7x, ₹ 9x$ and $₹ 12x$ respectively,and their expenditures be $₹ 8y, ₹ 9y$ and $₹ 15y$ respectively.Given that $A$ saves one-fourth of his income,so $A$'s saving $= \frac{1}{4} 	imes 7x = \frac{7x}{4}$.Since $	ext{Saving} = 	ext{Income} - 	ext{Expenditure}$,for $A$ we have: $7x - 8y = \frac{7x}{4}$.$28x - 32y = 7x \Rightarrow 21x = 32y \Rightarrow y = \frac{21x}{32}$.Now,calculate the savings for $B$ and $C$:$B$'s saving $= 9x - 9y = 9x - 9(\frac{21x}{32}) = 9x(1 - \frac{21}{32}) = 9x(\frac{11}{32}) = \frac{99x}{32}$.$C$'s saving $= 12x - 15y = 12x - 15(\frac{21x}{32}) = \frac{384x - 315x}{32} = \frac{69x}{32}$.The ratio of savings of $A, B$ and $C$ is $\frac{7x}{4} : \frac{99x}{32} : \frac{69x}{32}$.Multiplying by $32$,we get $56x : 99x : 69x$,which simplifies to $56: 99: 69$.

The incomes of $A, B$ and $C$ are in the ratio $7: 9: 12$ and their expenditures are in the ratio $8: 9: 15$. If $A$ saves one-fourth of his income,then the ratio of the savings of $A, B$ and $C$ is:

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