Quant · Arithmetic

Averages, Mixtures and Alligation

3 sub-topics · 22 lessons · 62 questions · 19 PYQs

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Averages9 lessons · 30 questions · 10 PYQs

Max and Min under an Average5 lessons · 13 questions · 4 PYQs

Mixtures and Alligation8 lessons · 19 questions · 5 PYQs

Formula sheet

Top half exceeds bottom half by a gap
$T-B=k\,d\Rightarrow T+B=2T-kd$
Alligation rule
$\frac{q_1}{q_2}=\frac{c_2-m}{m-c_1}\quad(c_1<m<c_2)$
Sum from an average
$\text{sum}=\text{average}\times n$
Weighted average of two groups
$\bar x=\frac{n_1\bar x_1+n_2\bar x_2}{n_1+n_2};\quad\frac{n_1}{n_2}=\frac{\bar x_2-\bar x}{\bar x-\bar x_1}$
Copper in mixed alloys
$\text{copper in a mix}=\sum w_i\frac{c_i}{c_i+z_i}$
Average of an arithmetic progression
$\text{AP: average}=\frac{\text{first}+\text{last}}{2}$
Largest value among distinct integers
$\text{distinct, smallest }s:\ \max=n\bar x-\left[s+(s+1)+\dots+(s+n-2)\right]$
Water to dilute a mixture
$\text{water added}=V\left(\frac pq-1\right)\ \text{for milk }p\%\to q\%$