Ocegik / Arithmetic
Arithmetic Formulas for CAT Preparation
Revise arithmetic formulas from Ocegik’s formula library, with named identities, expressions and usage notes grouped by topic.
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Arithmetic: formulas by topic
PercentagesArithmetic
Successive percentage change(a + b + ab100)%two successive changes of a% and b%
A is r% more/less than BB is 100r100 ± r% less/more than A
Simple & Compound InterestArithmetic
Simple InterestSI = P × r × n100P = principal, r% = annual rate, n = years
Compound Interest amountA = P(1 + r100)n
AmountA = Principal + Interest
Population growthP′ = P(1 + r100)nP = original population, P′ = population after n years
CI − SI, 2 years(CI)2 − (SI)2 = Pa2a = r/100
CI − SI, 3 years(CI)3 − (SI)3 = Pa2(a + 3)
Time to become Y times at SIyears = Y − 1X − 1 × Tgiven it becomes X times in T years
Time to become Y times at CIyears = T × n, where Xn = Y
Profit, Loss & DiscountArithmetic
Profit percentageProfit % = ProfitCP × 100
Selling priceSP = CP + P% of CP = CP(1 + P100)
DiscountDiscount = Marked Price − Selling Price
Discount percentageDiscount % = DiscountMarked Price × 100
Equal SP, one at +X% one at −X%net loss = X2100%
Ratio & ProportionArithmetic
Proportiona : b :: c : d ⇒ ad = bc
a < b, x positivea/b < (a+x)/(b+x) and a/b > (a−x)/(b−x)
a > b, x positivea/b > (a+x)/(b+x) and a/b < (a−x)/(b−x)
Componendo Lawif a/b = c/d, then (a+b)/b = (c+d)/d
Dividendo Law(a−b)/b = (c−d)/d
Componendo & Dividendo Law(a+b)/(a−b) = (c+d)/(c−d)
±c/±d ratio identity(a ± c)/(b ± d) = a/b
Chained equal ratios (=K)if a/b = c/d = e/f = K, then (a+c+e)/(b+d+f) = K
Weighted chained ratios(pa + qc + re)/(pb + qd + rf) = Kp, q, r are any weights, not all zero
Alligation, Mixtures & MeansArithmetic
Alligation rulew1 : w2 = (x2 − x) : (x − x1)weights inversely proportional to distance from the mean
Arithmetic MeanAM = x1 + x2 + … + xnn
Geometric MeanGM = ⁿ√(x1 × x2 × … × xn)
Harmonic MeanHM = n1/x1 + 1/x2 + … + 1/xn
Repeated dilutionK = K0(V − xV)nK₀ initial conc., V volume, x volume replaced each time
Time, Speed & DistanceArithmetic
Unit conversion1 km/hr = 5/18 m/s, 1 m/s = 18/5 km/hr
Average speed= Total DistanceTotal Time
Average speed, constant distanceSavg = 2S1S2S1 + S2harmonic mean of the two speeds
Average speed, constant timeSavg = S1 + S22arithmetic mean of the two speeds
Boats & streamsD = B + R, U = B − RD = downstream speed, U = upstream speed, B = boat's speed in still water, R = stream speed
Boat speed / stream speedB = D + U2, R = D − U2
Equal downstream/upstream distanceTimedown/Timeup = Upstream speed / Downstream speed
Clock angleθ = |30H − 112M|H = hours, M = minutes
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