Rapid Revision · Quantitative Aptitude
Alligation is weighted averages drawn as a cross. It answers one question fast: in what ratio do I mix cheap and dear to hit a target value?
If you read nothing else tonight, read these 6 lines.
Every formula for mixtures & alligation in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
Rule of alligation
(cheaper qty) : (dearer qty) = (dearer price - mean) : (mean - cheaper price)
Mean price
mean = (c1 x q1 + c2 x q2) / (q1 + q2)
Weighted average of the two ingredient prices.
Repeated replacement
final pure amount = initial x (1 - x/V)^n
Remove x from a V-litre vessel and top up with water, n times.
Two-stage read
alligation also solves ratios of profit%, speed, concentration, not just price
7 cards, each one idea: what it is, a worked example, and the trap to dodge.
To hit mean m by mixing values c (cheap) and d (dear): ratio cheap:dear = (d - m):(m - c).
Rice at 30 and 40 mixed to cost 34: ratio = (40-34):(34-30) = 6:4 = 3:2.
Trap: Read the ratio toward the OPPOSITE value: the (d - m) part belongs to the cheaper ingredient.
The target value must sit between the two ingredient values; if not, the mixture is impossible and you misread the question.
You cannot mix 20% and 30% solutions to get 35%.
Treat concentrations as the values in the cross. Pure water is 0%, pure milk or acid is 100%.
20% and 50% solutions to make 30%: ratio = (50-30):(30-20) = 2:1.
Remove k liters from V liters and replace with water, n times: remaining original = V x (1 - k/V)^n.
40 L milk, replace 4 L with water twice: 40 x (0.9)^2 = 32.4 L milk.
Trap: The formula gives the ORIGINAL liquid left, not the water added.
Adding pure water only changes the denominator. Milk stays fixed: new concentration = milk / new total.
10 L of 90% milk diluted to 60%: milk 9 L fixed, total must be 15 L, add 5 L water.
Selling a milk-water mix at the cost price of milk: gain% = (water / milk) x 100.
1 part water added to 4 parts milk, sold at cost: gain = 1/4 x 100 = 25%.
Trap: Gain is water over MILK, not water over total mixture.
When both inputs are already mixtures, track ONE component's amount through the blend, then recompute its share.
Equal volumes of 40% and 60% syrup: component = 0.4 + 0.6 = 1 per 2 L, so 50%.
A recap is not practice. These are the creators we rate for real depth on mixtures & alligation; full credit to each.
Each recap takes 3 minutes; the full set covers everything the first round tests. And when the test is cleared, your resume takes the next screen.
Original content by OptiResume; facts and formulas are common knowledge, the wording is ours. Go-deeper links go to creators we rate; we are not affiliated with them.