Mathematics - CBT 1 Numerical Ability
What the domain tests
Mathematics in RRB JE CBT 1 is Class 10 level arithmetic plus light algebra, geometry and trigonometry, compressed into a paper shared with reasoning, science and awareness. Expect number system, HCF/LCM, percentage, ratio-proportion, average, profit and loss, simple and compound interest, time-work and pipes, time-speed-distance, mensuration 2D/3D, and basic trigonometric identities.
Rules worth memorising cold
- Successive percentage change: net change = a + b + ab/100, keeping signs (a discount of 20% then 10% gives −28%).
- Compound interest, 2 years: CI = P[(1 + r/100)² − 1]. Simple interest stays on the original principal every year.
- Work problems: convert every worker or pipe to a rate (fraction of job per hour) and add rates; a drain or leak is subtracted.
- Train crossing a platform: distance = train length + platform length; relative speed adds when two trains run opposite, subtracts when same direction.
- Mensuration: cone = (1/3)πr²h, sphere surface = 4πr², cylinder curved surface = 2πrh.
Worked example
One pipe fills a tank in 12 h, a second in 18 h, and a drain empties it in 9 h. With all three open, take rates: 1/12 + 1/18 − 1/9. LCM of 12, 18 and 9 is 36, giving 3 + 2 − 4 = 1 part per 36 h. Net rate is 1/36 per hour, so the tank fills in 36 hours.
Traps that cost marks
Reading "A is 25% more than B" as B = 0.75A; the correct relation is B = A/1.25 = 0.8A. Forgetting to convert km/h to m/s by ×5/18. Using the CI formula where the question says simple interest. Mixing sin²θ + cos²θ = 1 with 1 + tan²θ = sec²θ. And ignoring that diameter is given where radius is needed - the single most common mensuration error.