The income 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.Let the spendings of $A, B$ and $C$ be $8y, 9y$ and $15y$ respectively.Given

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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.Let the spendings of $A, B$ and $C$ be $8y, 9y$ and $15y$ respectively.Given that $A$ saves $\frac{1}{4}$th of his income,so his saving is $\frac{7x}{4}$.Since $	ext{Saving} = 	ext{Income} - 	ext{Spending}$,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 $= 9x - 9y = 9x - 9(\frac{21x}{32}) = 9x - \frac{189x}{32} = \frac{288x - 189x}{32} = \frac{99x}{32}$.$C$'s saving $= 12x - 15y = 12x - 15(\frac{21x}{32}) = 12x - \frac{315x}{32} = \frac{384x - 315x}{32} = \frac{69x}{32}$.Ratio of savings of $A, B$ and $C = \frac{7x}{4} : \frac{99x}{32} : \frac{69x}{32}$.Multiply by $32$ to simplify: $(\frac{7x}{4} 	imes 32) : (\frac{99x}{32} 	imes 32) : (\frac{69x}{32} 	imes 32) = 56x : 99x : 69x$.Thus,the ratio is $56: 99: 69$.

The income of $A, B$ and $C$ are in the ratio $7: 9: 12$ and their spendings are in the ratio $8: 9: 15$. If $A$ saves $\frac{1}{4}$th of his income,then the savings of $A, B$ and $C$ are in the ratio of:

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