Quant · Arithmetic

Ratio, Proportion, Variation and Partnership

4 sub-topics · 34 lessons · 75 questions · 20 PYQs

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Ratios15 lessons · 33 questions · 14 PYQs

Proportion and Variation8 lessons · 18 questions · 2 PYQs

Partnership6 lessons · 12 questions · 2 PYQs

Problems on Ages5 lessons · 12 questions · 2 PYQs

Formula sheet

Combining two ratios
$a:b=p:q,\ b:c=r:s\Rightarrow a:b:c=pr:qr:qs$
Equal multiples to a ratio
$kA=mB=nC\Rightarrow A:B:C=\frac1k:\frac1m:\frac1n$
Partly fixed, partly variable
$\text{total}=F+vn$
When did a partner join
$\frac{C_1\times12}{C_2\times(12-x)}=\frac{P_1}{P_2}$
Joint variation
$x\propto\frac{y^a}{z^b}\Rightarrow x=K\frac{y^a}{z^b}$
Adding the same number to both terms
$\frac ab<1\Rightarrow\frac ab<\frac{a+k}{b+k}<1\quad(k>0)$
Componendo-dividendo
$\frac ab=\frac cd\Rightarrow\frac{a+b}{a-b}=\frac{c+d}{c-d}$
Pairwise sums in a ratio
$(a+b):(b+c):(c+a)=p:q:r\Rightarrow a+b+c=\frac{p+q+r}{2}\,k$