MAH CET MCA Ratio Proportion And Variation Previous Year Questions (PYQs)
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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
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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 $= 56 : 99 : 69$.
Birds on trees $A$ and $B$ say: if $2$ from $B$ move to $A$, numbers are equal; if $2$ from $A$ move to $B$, then $B$ becomes double of $A$. Find numbers on $A,B$.
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Solution
Let $A=x,\ B=y$.
$x+2=y-2\Rightarrow y=x+4$.
$y+2=2(x-2)\Rightarrow y=2x-6$.
Solving: $x=10,\ y=14$.
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