Formula Sheet
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Quant Formula Sheet

Use this as your last-day formula sheet.

Percentages

x% = x/100

  • x% of y = xy/100
  • Increase from A to B: ((B - A) / A) × 100
  • Decrease from A to B: ((A - B) / A) × 100
  • If price increases by x%, new value = old × (100 + x)/100
  • If price decreases by x%, new value = old × (100 - x)/100

Successive percentage change

Net change for +a% and +b%:

a + b + ab/100

For +a% then -b%:

a - b - ab/100

Example: +20% then -10% = 20 - 10 - 2 = +8%.

Profit, Loss, Discount

  • Profit = SP - CP
  • Loss = CP - SP
  • Profit % = (Profit / CP) × 100
  • Loss % = (Loss / CP) × 100
  • Discount = MP - SP
  • Discount % = (Discount / MP) × 100

If marked price is MP and discount is d%:

SP = MP × (100 - d)/100

Simple Interest

SI = PRT/100
Amount = P + SI

Where:

  • P = principal
  • R = annual rate
  • T = time in years

Compound Interest

A = P(1 + R/100)^T
CI = A - P

For 2 years:

CI = P × [2R/100 + (R/100)^2]

Ratio and Proportion

If A:B = m:n, take:

A = mx, B = nx

If values are divided in ratio a:b:c, total parts = a+b+c.

Share of first part:

total × a/(a+b+c)

Averages

Average = Sum / Number of items
Sum = Average × Number of items

If one number is replaced:

New average = Old average + (new value - old value)/n

Time and Work

If A completes work in x days:

A's one-day work = 1/x

If A and B work together:

1/x + 1/y = (x+y)/(xy)
Days together = xy/(x+y)

Efficiency is inverse of time:

Efficiency ratio A:B = y:x

if A takes x days and B takes y days.

Pipes and Cisterns

  • Inlet pipe = positive work
  • Outlet pipe = negative work

If inlet fills in x hours and outlet empties in y hours:

Net work/hour = 1/x - 1/y
Time = 1 / net work

Time, Speed, Distance

Speed = Distance / Time
Distance = Speed × Time
Time = Distance / Speed

Unit conversion:

km/h to m/s = × 5/18
m/s to km/h = × 18/5

Relative speed:

  • Same direction: difference
  • Opposite direction: sum

Train crossing pole:

Time = train length / speed

Train crossing platform:

Time = (train length + platform length) / speed

Boats and Streams

Downstream speed = boat speed + stream speed
Upstream speed = boat speed - stream speed
Boat speed = (downstream + upstream)/2
Stream speed = (downstream - upstream)/2

Number System

  • Even number: divisible by 2
  • Odd number: not divisible by 2
  • Prime number: exactly two factors, 1 and itself
  • Composite number: more than two factors
  • Co-prime: GCD is 1

Divisibility:

  • 2: last digit even
  • 3: sum of digits divisible by 3
  • 4: last two digits divisible by 4
  • 5: last digit 0 or 5
  • 6: divisible by 2 and 3
  • 8: last three digits divisible by 8
  • 9: sum of digits divisible by 9
  • 10: last digit 0
  • 11: difference between alternating digit sums divisible by 11

LCM and HCF

For two numbers:

Product = LCM × HCF

Use HCF for:

  • largest possible equal size,
  • maximum length,
  • greatest common divisor.

Use LCM for:

  • events repeating together,
  • least common time,
  • minimum number exactly divisible.

Probability

Probability = favorable outcomes / total outcomes

At least one:

P(at least one) = 1 - P(none)

Permutation and Combination

Permutation: arrangement/order matters.

nPr = n! / (n-r)!

Combination: selection/order does not matter.

nCr = n! / [r!(n-r)!]

Data Interpretation

Core operations:

  • percentage share,
  • increase/decrease,
  • average,
  • ratio,
  • total difference.

Shortcut:

Read the question first, then table/chart. Do not fully analyze the chart before knowing what is asked.