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Previous Year Question (PYQs)
4
The incomes of $A$, $B$ and $C$ are in the ratio $7 : 9 : 12$ and their spending are in the ratio $8 : 9 : 15$. If $A$ saves $\dfrac{1}{4}$ of his income, then the savings of $A$, $B$ and $C$ are in the ratio of
Solution
Let incomes be $7x, 9x, 12x$ and expenditures be $8y, 9y, 15y$.
Saving of $A = 7x - 8y = \dfrac{1}{4}(7x) \Rightarrow 7x - 8y = \dfrac{7x}{4} \Rightarrow 8y = \dfrac{21x}{4} \Rightarrow y = \dfrac{21x}{32}$.
Savings:
$A = \dfrac{7x}{4}$,
$B = 9x - 9y = 9x - 9\left(\dfrac{21x}{32}\right) = \dfrac{99x}{32}$,
$C = 12x - 15y = 12x - 15\left(\dfrac{21x}{32}\right) = \dfrac{69x}{32}$.
Hence ratio $= 56 : 99 : 69$.
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