Rapid Revision · Quantitative Aptitude
Ratios are the grammar of quant: ages, mixtures, partnerships and speeds all speak it. Two moves matter, combining ratios and splitting totals.
If you read nothing else tonight, read these 6 lines.
Every formula for ratio & proportion in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
Ratio & proportion
a : b = a / b a : b :: c : d => a x d = b x c
Split N in a : b
parts = N x a / (a + b) and N x b / (a + b)
Combine a:b and b:c
a : b : c (scale so the shared term b matches)
Mean proportional
mean proportional of a and c = sqrt(a x c)
Componendo-dividendo
if a/b = c/d then (a + b)/(a - b) = (c + d)/(c - d)
Duplicate ratios
duplicate = a^2 : b^2 sub-duplicate = sqrt(a) : sqrt(b)
8 cards, each one idea: what it is, a worked example, and the trap to dodge.
Given a:b and b:c, scale both so the b values match (use the LCM), then chain into a:b:c.
a:b = 2:3 and b:c = 4:5. LCM of 3 and 4 is 12: a:b:c = 8:12:15.
Trap: Do not glue 2:3 and 4:5 into 2:3:5; the shared term must match first.
Total T split in ratio p:q:r gives shares T x p/(p+q+r), T x q/(p+q+r), T x r/(p+q+r).
720 in 2:3:4: parts sum to 9, so shares are 160, 240, 320.
a/b = c/d exactly when ad = bc. Use it to solve for one unknown in a proportion instantly.
x/12 = 15/20: x = 12 x 15 / 20 = 9.
b is the mean proportional between a and c when b^2 = ac, so b = sqrt(ac).
Mean proportional of 4 and 16 = sqrt(64) = 8.
a:b is not (a+x):(b+x). Set up the equation with the unknown multiplier k: the quantities are ak and bk.
Ratio 3:4, add 6 to each, new ratio 4:5: 3k+6 / 4k+6 = 4/5 gives k = 6, numbers 18 and 24.
Trap: Never cancel the +x; ratios only cancel common FACTORS, not common terms.
If a/b = c/d then (a+b)/(a-b) = (c+d)/(c-d). It removes messy algebra in one line.
(x+y)/(x-y) = 5/1 means x/y = 3/2 (apply the rule backwards).
Count and value are different ratios. Convert counts to value using each coin's worth, then match the total.
1-rupee, 50-p, 25-p coins in count ratio 2:3:4 worth Rs 45: value ratio 2 : 1.5 : 1, so units of 4.5 -> multiplier 10: 20, 30, 40 coins.
Trap: Multiplying the count ratio by the total directly ignores coin values.
Profit divides in the ratio of (capital x time) for each partner.
A puts 5000 for 12 months, B 6000 for 10 months: 60000:60000 = 1:1, equal shares.
A recap is not practice. These are the creators we rate for real depth on ratio & proportion; 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.