NISM SSC, Quantitative Aptitude. Updated Jun 2026, 13-minute read.

SSC CGL Quantitative Aptitude — Shortcuts for Arithmetic Topics

SSC CGL Tier 2 has 30 Maths questions worth 90 marks (3 marks each) with 0.5 negative marking. The high marks per question means accuracy matters more than speed — don't guess on maths.

Key takeaways

Profit & Loss: use multiplier method — 20% profit → multiplier 1.2; 15% loss → multiplier 0.85
Time-Speed-Distance: when speed changes, use relative speed for opposite direction (sum) and same direction (difference)
CI vs SI: for 2 years, CI − SI = P × (r/100)². For 3 years, CI − SI = P(r/100)²(3 + r/100)
Ratio & Proportion: use component dividendo method for complex fractions; unit price method for mixture problems
Time & Work: use LCM method — assume total work = LCM of days; find per-day work as fraction
Geometry: sin²θ + cos²θ = 1; tan²θ + 1 = sec²θ; 1 + cot²θ = cosec²θ — memorise all 3
Mensuration: area of trapezoid = ½(a+b)×h; volume of cone = ⅓πr²h; sphere = 4/3πr³

Profit and Loss

Key Formula: Profit % = (Profit/CP) × 100. Loss % = (Loss/CP) × 100.

Multiplier Method (Fastest Approach)

Convert % to multiplier: SP = CP × multiplier

20% profit: SP = CP × 1.20
15% loss: SP = CP × 0.85
12.5% profit: SP = CP × 1.125 = CP × 9/8

Successive Discounts

Two successive discounts of a% and b% = Net discount = (a + b − ab/100)%

Example: 20% then 10% → Net = 20 + 10 − (20×10)/100 = 30 − 2 = 28% discount

Dishonest Shopkeeper Problems

Shopkeeper uses wrong weights but claims correct price → Profit% = (True Weight − False Weight)/False Weight × 100

Example: Claims 1 kg but gives 800g → Profit = 200/800 × 100 = 25%

Time, Speed and Distance

Basic Formula: Distance = Speed × Time. All three must be in consistent units.

Train Problems

Train crossing a pole/person: Time = Length of Train / Speed
Train crossing a platform: Time = (Length of Train + Length of Platform) / Speed
Two trains opposite direction: Relative speed = S₁ + S₂; Time to cross = (L₁ + L₂)/(S₁+S₂)
Two trains same direction: Relative speed = |S₁ − S₂|; Time = (L₁ + L₂)/|S₁−S₂|

Average Speed

For same distance at two speeds: Average speed = 2ab/(a+b)

Critical note: Average speed ≠ (a+b)/2. This is a very common trap in SSC exams.

Simple Interest and Compound Interest

SI = P × R × T / 100

CI = P × (1 + R/100)^T − P

Key shortcuts

For 2 years: CI − SI = P × (R/100)²
At 10% for 2 years: CI = 21% of P, SI = 20% of P → Difference = 1% of P
Doubling time at R% CI ≈ 72/R years (Rule of 72)

Time and Work

LCM Method

A can do work in 12 days, B in 15 days. Together?

LCM(12, 15) = 60 units (total work)
A does 60/12 = 5 units/day; B does 60/15 = 4 units/day
Together: 9 units/day → Complete in 60/9 = 6.67 days

Pipe and Cistern

Filling pipe adds work; draining pipe removes work. Use same LCM method with negative value for draining pipe.

Trigonometry

Standard values table

Angle	sin	cos	tan
0°	0	1	0
30°	1/2	√3/2	1/√3
45°	1/√2	1/√2	1
60°	√3/2	1/2	√3
90°	1	0	∞

Frequently asked questions

How to remember sin, cos, tan values?

Use 'Some People Have Curly Black Hair Through Proper Brushing' — for sin: 0, 1/2, 1/√2, √3/2, 1. For cos, reverse the sin values. For tan = sin/cos.

How many marks does Arithmetic vs Geometry carry in SSC CGL Tier 2?

In SSC CGL Tier 2 QA (30Q, 90 marks), approximately: Arithmetic topics (Profit-Loss, CI/SI, TSD, T&W, Ratio) = 12–15 questions. Geometry + Mensuration + Trigonometry = 8–10 questions. Algebra = 3–5 questions. DI = 3–5 questions.

Written by Arpan Das.

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