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?

  1. LCM(12, 15) = 60 units (total work)
  2. A does 60/12 = 5 units/day; B does 60/15 = 4 units/day
  3. 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

Anglesincostan
0°010
30°1/2√3/21/√3
45°1/√21/√21
60°√3/21/2√3
90°10∞