RRB NTPC (Non-Technical Popular Categories): Graduate and Undergraduate Posts

Percentage and Fractions

• Fraction table1/2 = 50%, 1/3 = 33⅓%, 1/4 = 25%, 1/6 = 16⅔%, 1/8 = 12.5%, 1/12 = 8⅓%
• Successive changeNet % = a + b + ab/100
• Price up r%, keep spend sameCut consumption by r/(100 + r) × 100%
• A is r% more than BB is r/(100 + r) × 100% less than A

💡 Convert percentages to fractions before calculating: 37.5% of 640 is 3/8 × 640 = 240.

Profit, Loss and Discount

• Profit %(SP − CP)/CP × 100
• Marked priceSP = MP × (1 − d/100)
• Mark-up m%, discount d%Profit % = m − d − md/100
• Successive discountsSingle equivalent = d₁ + d₂ − d₁d₂/100
• False weightGain % = error/(true value − error) × 100

💡 Profit and loss % are always on CP; discount % is always on MP.

Simple and Compound Interest

• SISI = P × R × T/100
• Amount (CI)A = P(1 + R/100)ᵀ
• CI − SI, 2 yearsP × (R/100)²
• CI − SI, 3 yearsP × (R/100)² × (3 + R/100)
• Half-yearlyRate R/2, time 2T

💡 At 10% for 2 years, CI is 21% of P and SI is 20%: the gap is 1% of P.

LCM, HCF and Number System

• Two numbersLCM × HCF = product of the numbers
• FractionsLCM = LCM of numerators/HCF of denominators; HCF = HCF of numerators/LCM of denominators
• Ratio a:b with HCF xNumbers ax and bx, LCM = abx (a, b co-prime)
• Divisibility by 11(sum of odd-place digits) − (sum of even-place digits) = 0 or a multiple of 11
• Unit digit cycles2: 2,4,8,6; 3: 3,9,7,1; 7: 7,9,3,1; 8: 8,4,2,6

💡 Bells or lights 'together again' questions are always LCM; 'largest size that divides exactly' is always HCF.

Average, Ratio and Ages

• AverageSum = average × number of items
• ReplacementNew item = old item + (change in average × n)
• Consecutive numbersAverage = middle term (or mean of first and last)
• Mean proportional of a, b√(ab)
• PartnershipProfit share ∝ capital × time

💡 Work with sums, not averages: write sum before and sum after, then subtract.

Time and Work, Pipes

• RateIf A takes a days, A's one-day work = 1/a
• TogetherA and B together = ab/(a + b) days
• LCM methodTotal work = LCM of days; efficiency = total/days
• PipesFilling pipe +, leak or outlet −
• Partial workIf 2/5 of a job takes 12 days, the full job takes 12 × 5/2 = 30 days

💡 Always convert 'part of the work in d days' to full-job days before adding rates.

Speed, Distance and Trains

• BasicDistance = speed × time; km/h × 5/18 = m/s
• Train passes a poleTime = length of train/speed
• Train passes a platformTime = (train + platform length)/speed
• Relative speedOpposite directions: add; same direction: subtract
• Average speed (equal distances)2xy/(x + y)
• BoatsDownstream = u + v, upstream = u − v

💡 Convert units first: most wrong answers in train questions come from mixing km/h and m/s.

Mensuration

• CircleArea πr², circumference 2πr
• CylinderVolume πr²h, CSA 2πrh, TSA 2πr(r + h)
• ConeVolume ⅓πr²h, CSA πrl, l = √(r² + h²)
• SphereVolume (4/3)πr³, surface area 4πr²
• HemisphereVolume (2/3)πr³, CSA 2πr², TSA 3πr²
• Triangle (Heron)√(s(s − a)(s − b)(s − c)), s = (a + b + c)/2

💡 Check whether the question gives diameter or radius: halve it before squaring.

Algebra and Trigonometry

• Identities(a + b)² = a² + 2ab + b²; a² − b² = (a + b)(a − b)
• Cubesa³ + b³ = (a + b)(a² − ab + b²); if a + b + c = 0 then a³ + b³ + c³ = 3abc
• Pythagorean identitysin²θ + cos²θ = 1; sec²θ − tan²θ = 1
• Standard valuessin 30° = ½, sin 45° = 1/√2, sin 60° = √3/2, tan 45° = 1
• Triplets3-4-5, 5-12-13, 8-15-17, 7-24-25

💡 If sin θ = 5/13, use the 5-12-13 triplet: cos θ = 12/13 and tan θ = 5/12 without any calculation.